Annotated Bibliography on The Evolution of Cooperation

Introduction

This guide includes work that makes use of Robert Axelrod's The Evolution of Cooperation (NY: Basic Books, 1984) or earlier work included in that book, such as the biological article by Robert Axelrod and William Hamilton of the same title in Science, vol. 211 (1981): 1390-96. While most of the items included in this bibliography explicitly cite this work, other research which draws heavily on the ideas and themes of Axelrod's approach is also cited here. This bibliography generally excludes work that makes only passing or minor reference to Axelrod.

We apologize to authors whose contributions we may have overlooked.

• PD: (iterated) Prisoner's Dilemma
• TFT: Tit-for-Tat
• ESS: Evolutionary (or Evolutionarily) Stable Strategy

This project was supported by the University of Michigan LSA College Enrichment Fund.

Keywords

• Assumptions and Concepts:
• Choices (if choices other than the two choices of cooperate or defect)
• Endogenous ending
  • voluntary exit (players may choose to exit the game)
  • ostracism
• Interactions (if greater than two players)
• Limited set of allowable rules
  • enumerated set (the work considers specific defined strategies such as TFT)
  • finite state machines (automata)
  • limited rationality
  • parameterized rules (allowable rules are specified by particular parameters)
• Noise
  • misimplementation (when the player makes a mistake implementing its choice)
  • misperception (when one player misperceives the other player's signal or choice)
• Norms
• Payoffs (also used when the work compares PD to other games)
• comparing PD matrices (used when the work compares different forms or versions of the PD)
• Population dynamics
• ESS
  • replicator dynamics (involving changing proportions of rules based on their success)
  • population size (distinguished from Interactions in that relations among players are bilateral, or population size is an independent factor)
• Population structure (non-random interactions)
  • information requirements (interact with others based on observable characteristics or signals)
  • clustering (tendency to interact with own type)
  • spatial models (local interactions or interactions with neighbors)
• Relative vs. absolute gains
• Reputation

Applications:

• Automata theory (including computer science)
• Biological applications
• Politics and Law, Domestic
• Politics and Law, International
• Economics and business
• Miscellaneous
• Psychology
• Sociology and anthropology
• Theory (including evolutionary theory)

Type:

• Biological applications - specific species (empirical studies of specific animals or insects)
• Deductive
• Empirical (includes qualitative and quantitative studies of humans, organizations, or use of archival data)
• Simulation (has a predefined universe of rules)
• Tournament (has submitted rules)

OTHER:

• Collateral research (work that does not directly build on Axelrod's, but is related to the concepts and assumptions in his work)

• 1. Abbott, Kenneth W. 1989. "Modern International Relations Theory: A Prospectus for International Lawyers." Yale Journal of International Law 14:335-411.
  • A review of leading contributions to the field of international relations and their relevance to international law. International law has fallen behind other law fields in developing an analytical approach; by linking the work in international relations to international law, Abbott hopes to suggest how international law might apply these tools theoretically and empirically. He reviews fundamental concepts, such as Waltz's three images of international relations and the rational actor approach. He discusses the contributions of game theory by describing a number of games, including Harmony, Deadlock, Stag Hunt, coordination games, and the PD. He argues that the PD illustrates why states seek cooperation, but also why it is so difficult to achieve. He considers examples of the PD in international relations, such as the security dilemma and competition to expand alliances, and notes the importance of repeated play and the magnitude of the payoffs to cooperation. Abbott suggests that norms such as proportionality embody the characteristics of TFT, and that regimes may help to alleviate states' monitoring problems. In the final section he discusses the Limited Test Ban and Nuclear Nonproliferation Treaties as legal means for the United States and the former Soviet Union to resolve PD situations. - abstract by LD Payoffs/Norms/Politics and law - international.
  
  
• 2. Abreu, Dilip, Paul Milgrom and David Pearce. 1991. "Information and Timing in Repeated Partnerships." Econometrica 59:1713-1733.
  • In a repeated partnership game with imperfect monitoring, [the authors] distinguish among the effects of (1) reducing the interest rate, (2) shortening the period over which actions are held fixed, and (3) shortening the lag with which accumulated information is reported. All three changes are equivalent in games with perfect monitoring. With imperfect monitoring, reducing the interest rate always increased the possibilities for cooperation, but the other two changes always have the reverse effect when the interest rate is small. Interactions/Payoffs/Noise/Economics and business/Theory/Deductive.
  
  
• 3. Akimov, Vladimir and Mikhail Soutchanski. 1994. "Automata Simulation of N-Person Social Dilemma Games." Journal of Conflict Resolution 38:138-148.
  • Collective behavior of N players in a social dilemma game is simulated by automata exhibiting cooperative behavior. In his models of simple biological systems, Tsetlin assumed minimum information available to the players. The automata in this study were somewhat more sophisticated, using Markov strategies in their interactions. The authors investigated relationships between information received by the automata and the emergence of cooperation in a simulated evolution process. In some ways, this approach is similar to that of Axelrod. However, instead of determining the most successful strategy, the authors seek surviving strategies in a social dilemma environment. Previous results showed that cooperation could be established asymptotically under partially centralized control. In this model there is no such control. The main result is that more sophisticated behavior of self-seeking automata compensates for the absence of such control Moreover, cooperation is established more rapidly when more information is available to the automata. Interactions/Limited set of allowable rules - finite state machines/Automata theory/Simulation.
• 4. Andreoni, James and John H. Miller. 1993. "Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence." Economic Journal 103:570-585.
  • In a finite repeated PD, defection is the dominant strategy for both players, but if players have incomplete information, then cooperation in early rounds of the game can be rational (i.e., it can be rational to pretend to be altruistic) in order to develop a reputation for cooperation. The authors use two sets of experiments to examine cooperation in a finitely repeated PD where subjects' beliefs about other players' types (how altruistic the other players are) is manipulated. They considered two questions: first, the sequential equilibrium reputation hypothesis, in which people rationally build reputations; and second, whether some proportion of the population actually has altruistic motives. The experimental results indicated that there was support for the sequential equilibrium reputation hypothesis; subjects seemed to try to build a reputation for altruism. There also appeared to be some people who were altruistic, based on a control group that player a series of single-shot PDs. The authors suggest that all models of altruism are some combination of three models: pure altruism, where players care about others' payoffs; duty, where players feel an obligation to cooperate; and reciprocal altruism. Focusing on reciprocal altruism, they argue that players do not have to be irrational or altruistic in order to cooperate, as long as they believe that other altruistic players exist in the population. They ran a second experiment, the results of which again supported a reputation building hypothesis, and were consistent with the claim that altruistic types exist within the population. abstract by LD Interactions/Population structure/Reputation/Empirical.
• 5. Aumann, Robert J. and Sylvain Sorin. 1989. "Cooperation and Bounded Recall." Games and Economic Behavior 1:5-39.
  • The authors suggest that some irrationality, such as a perturbation, must be built into the system in order to achieve cooperation. A primary conclusion here is that evolution in the simulations is not toward TFT. - LD A two-person game has common interests if there is a single payoff pair z that strongly Pareto dominates all other payoff pairs. Suppose such a game is repeated many times, and that each player attaches a small but positive probability to the other playing some fixed strategy with bounded recall, rather than playing to maximize his payoff. Then the resulting supergame has an equilibrium in pure strategies, and the payoffs to all such equilibria are close to optimal (i.e., to z). Payoffs/Limited set of allowable rules - limited rationality/Theory/Automata theory/Deductive.
• 6. Axelrod, Robert. 1992. "How to Promote Cooperation." Current Contents 24:10.
  • This "Citation Classic" report is a personal statement of the origins, development and effect of my work on cooperation. My interests in artificial intelligence and game theory, and a concern with international politics led to the development of the computer tournament for the Prisoner's Dilemma. I believe the work has been well cited because it fits a widespread desire to prove a "hardheaded" rationale for cooperation, because it is easy to understand, and because it is general enough to be applicable to a wide range of disciplines. - abstract by RA Politics and law - international/Tournament.
• 7. Axelrod, Robert and Douglas Dion. 1988. "The Further Evolution of Cooperation." Science 242:1385-1390.
  • Axelrod's model of the evolution of cooperation was based on the iterated Prisoner's Dilemma. Empirical work following this approach has helped establish the prevalence of cooperation based on reciprocity. Theoretical work has led to a deeper understanding of the role of other factors in the evolution of cooperation: the number of players, the range of possible choices, variation in the payoff structure, noise, the shadow of the future, population dynamics, and population structure. Interactions/Choices/Payoffs/Noise/Population dynamics/Population structure/Theory.
• 8. Badcock, Christopher. 1991. Evolution and Individual Behavior: An Introduction to Human Sociobiology. Oxford: Basil Blackwell.
  • An introductory text of recent applications of evolutionary theory to humans. The introduction provides a brief discussion of Darwin's thought on natural selection and reproductive success, and an overview of the puzzle of altruism and cooperation in evolutionary terms. Chapter 1 has a fairly extensive discussion of The Evolution of Cooperation, including the success of TFT, the emergence of cooperation in iterated play of the PD, and the evolution of altruism within clusters of discriminating individuals. Chapter 2 considers three different types of altruism (kin, reciprocal and induced) and maps four different types of social action between two people on to the four cells of the PD. Chapter 3 discusses the importance of being able to identify others as potential cooperators and how such recognition might have evolved. Other chapters in the book focus on male and female behaviors, the relationships between parents and children, the link between these results and Freud, and the nature of culture. - abstract by LD Interactions/Population structure - information requirements/Sociology and anthropology/Biological applications.
• 9. Bendor, Jonathan. 1993. "Uncertainty and the Evolution of Cooperation." Journal of Conflict Resolution 37:709-734.
  • It is well known that inferential errors can induce nice but provocable strategies to engage in vendettas with each other. It is therefore generally believed that imperfect monitoring reduces the payoffs of such strategies and impairs the evolution of cooperation. The current literature, however, only scrutinizes specific strategies, either analytically or in particular tournaments. This article examines in a more general way how monitoring uncertainty affects the fate of cooperation in tournaments of the iterated prisoner's dilemma (IPD). The first set of results shows that imperfect monitoring does create a sharp trade-off between cooperativeness and unexploitability. The second set examines how random shocks affect the tournament payoffs of several large classes of strategies in the IPD, and shows how noise can help certain nice strategies. The third set analyzes how imperfect monitoring can facilitate the emergence of cooperation based on a population of non-nice strategies. Thus the idea that inferential uncertainty always harms nice strategies and always impairs the evolution of cooperation must by sharply qualified. Payoffs - comparing different PD matrices/Noise - misimplementation/Noise - misperception/Population dynamics - ESS/Theory/Deductive.
• 10. Bendor, Jonathan, Roderick M. Kramer and Suzanne Stout. 1991. "When in Doubt. . .: Cooperation in a Noisy Prisoner's Dilemma." Journal of Conflict Resolution 35:691-719.
  • The results suggest that generosity in a noisy environment dampens unintended vendettas. - LD In the last decade, there has been a resurgence of interest in problems of cooperation, stimulated largely by Axelrod's work. Using an innovative tournament approach, Axelrod found that a simple strategy, tit-for-tat (TFT) was most successful in playing the repeated prisoner's dilemma (PD) in a noiseless environment. However, recent analytical work has shown that monitoring problems caused by noise significantly impair TFT's effectiveness. The primary purpose of the present approach is to discover whether there exist alternative strategies that perform well in noisy PDs. To investigate this question, the authors conducted a computer tournament. The results of the tournament demonstrated that, consistent with analytical work, TFT performed rather poorly. In contrast, strategies that were generous (i.e., cooperated more than their partners did) were quite effective. Noise/Psychology/Tournament.
• 11. Bendor, Jonathan and Dilip Mookherjee. 1987. "Institutional Structure and the Logic of Ongoing Collective Action." American Political Science Review 81:129-154.
  • Work by Axelrod, Hardin, and Taylor indicates that problems of repeated collective action may lessen if people use decentralized strategies of reciprocity to induce material cooperation. Hobbes's centralized solution may thus be overrated. [Bendor and Mookherjee] investigate these issues by representing ongoing collective action as an n-person repeated prisoner's dilemma. The results show that decentralized conditional cooperation can ease iterated collective action dilemmas - if all players perfectly monitor the relation between individual choices and group payoffs. Once monitoring uncertainty is introduced, such strategies degrade rapidly in value, and centrally administered selective incentives become relatively more valuable. Most importantly, [the authors] build on a suggestion of Herbert Simon by showing that a hierarchical structure, with reciprocity used in subunits and selective incentives centrally administered, combines the advantages of the decentralized and centralized solutions. The hierarchical form is more stable than the decentralized structure and often secures more cooperation than the centralized structure. Generally, the model shows that the logic of repeated decision making has significant implications for the institutional forms of collective action. Interactions/Payoffs/Noise/Population size/Population structure/Politics and law - domestic/Politics and law - international/Sociology and anthropology/Theory/Deductive.
• 12. Bendor, Jonathan and Dilip Mookherjee. 1990. "Norms, Third-Party Sanctions, and Cooperation." Journal of Law, Economics, and Organization 6:33-63.
  • Social norms aid in cooperation in three ways: decision makers internalize them; those injured by norm violations punish the violator; and unaffected third parties punish the violator of the norms. The authors consider here what third party interactions and sanctions contribute to cooperation beyond bilateral interactions and sanctions. Do such sanctions always facilitate cooperation, and when are such sanctions most effective? Under very restrictive conditions, third party sanctions did not contribute independently to cooperation beyond the effects of bilateral sanctions. Third party sanctions were effective when there was asymmetry in the pair relationship. They were effective in facilitating cooperation when interactions between different pairs of players were linked, and at intermediate values of the discount rate. The authors also explored the role of coalition size and exploitation of the majority by the minority. - abstract by LD Payoffs/Population size/Norms/Reputation/Theory/Deductive.
• 13. Betz, Brian. 1991. "Response to Strategy and Communication in an Arms Race-Disarmament Dilemma." Journal of Conflict Resolution 35:678-690.
  • Subjects (40 males and 40 females) played against a simulated other in a six-choice prisoner's dilemma game that was described in terms of an arms race. The simulated other employed either a GRIT or tit-for-tat strategy, with either communication or no communication. The GRIT strategy elicited more cooperation than the tit-for-tat strategy, and there was an interaction such that the GRIT strategy with communication produced more cooperation than any of the other conditions. In addition, explicit communication decreased the occurrence of deception being employed against the GRIT strategist. Although GRIT produced more conciliation than tit-for-tat, the simulated other using GRIT was also taken advantage of more frequently; to avoid exploitation, modifications in the GRIT strategy may be needed. The results are discussed in terms of how explicit communication is needed for GRIT to be optimally effective and how additional communication may reduce exploitation. Payoffs - comparing different PD matrices/Population structure - information requirements/Limited set of allowable rules - enumerated set/Politics and law - international/Empirical.
• 14. Bicchieri, Cristina. 1990. "Norms of Cooperation." Ethics 100:838-861.
  • Argues that instrumental rationality approaches are inadequate to explain how norms become established and why people adhere to them. Bicchieri suggests that an evolutionary approach to norms provides better answers to these questions. She defines social norms as "the outcome of learning in a strategic interaction context; hence, they are a function of individual choices and, ultimately, of individual preferences and beliefs" (p. 839). Norms are clusters of expectations, or conditional preferences which thus depend on the preferences of others. Because of this dependence on other's preferences, norms are better modeled as a coordination game rather than a zero sum game. Examining the two and n-person PDs, Bicchieri explores the conditions under which cooperation is rational. She argues that once a cooperative equilibrium is established, it is likely to persist because future decisions will be based on past choices. Yet establishing cooperation in a large group is likely to be difficult since individual choice has a negligible effect on the outcome and defection can go undetected. Bicchieri proposes that cooperation can become well established in small groups and then diffuse through an evolutionary process to larger groups. - abstract by LD Interactions/Payoffs - comparing different PD matrices/Noise - misperception/Population dynamics - replicator dynamics/Population structure - information requirements/Norms/Limited set of allowable rules - limited rationality/Deductive.
• 15. Binmore, Kenneth and Larry Samuelson. 1992. "Evolutionary Stability in Repeated Games Played by Finite Automata." Journal of Economic Theory 57:278-305.
  • [The authors] consider a game in which "meta-players" choose finite automata to play a repeated stage game. Meta-players' utilities are lexicographic, first increasing in the (limit-of-the-means) payoffs of the repeated game and second decreasing in the number of states in their automaton. [The authors] examine the outcomes in this game which satisfy a version of evolutionary stability that has been modified to permit existence. [The authors] find that such automata must be efficient, in that they must maximize the sum of the (limit-of-the-means) payoffs from the repeated game. Population dynamics - ESS/Population structure - information requirements/Limited set of allowable rules - finite state machines/Limited set of allowable rules - limited rationality/Automata theory/Theory/Deductive/Simulation.
• 16. Bolle, Friedel and Peter Ockenfels. 1990. "Prisoners' Dilemma as a Game with Incomplete Information." Journal of Economic Psychology 11:69-84.
  • The Prisoners' Dilemma is reformulated as a game (with incomplete information) between players of different 'moral standards'. Equilibrium solutions are computed for games with simultaneous choices and for games with sequential choices. Cooperation should occur more frequently in the latter. Experiments are conducted with both types of games. The results can neither be explained by (linear) altruistic utility functions nor by a revaluation of the cooperative choices. They can be explained, however, by a revaluation of the cooperative result. In this case [the authors] get an extreme distribution of the 'moral standards'. Expressed as monetary values and compared with the monetary rewards of the game there seems to be one class of persons with rather high standards, another class of persons with rather low standards, and practically no intermediate cases. The rejection of altruistic utility functions as well as the rejection of certain norms of behavior have important consequences for the implementation of altruism, norms and morals in formal models of decision making. Payoffs - comparing different PD matrices/Norms/Theory/Psychology/Deductive/Empirical.
• 17. Borstnik, B., D. Pumpernik, I. L. Hofacker and G. L. Hofacker. 1990. "An ESS-analysis for Ensembles of Prisoner's Dilemma Strategies." Journal of Theoretical Biology 142:189-200.
  • The ESS (Evolutionary Stable Strategy) concept of Maynard Smith can be applied in its weak form to ensembles of competing PD ("Prisoner's Dilemma") strategies memorizing two to three of one's own and one's opponent's moves. The format of our study is:
    • (1) games have very long duration;
    • (2) Taylor-Jonker dynamics applies;
    • (3) Effects of finite population size can be ignored.
    It is shown that in the case R>(T+S)/2 a set of strategies can be singled out which do not lose against any other strategy while co-operating with themselves. Such a set is uninvadable by other PD strategies if it constitutes more than half of the total population. Population dynamics - ESS/Population dynamics - replicator dynamics/Simulation.
• 18. Bower, B. 1992. "Cooperation Evolves in Computer Tourney." Science News 141:39.
  • Discusses the results from M. Nowak and K. Sigmund (1992) "Tit for Tat in Heterogeneous Populations." Nature 355:250-253. See also H.C.J. Godfray (1992) "The Evolution of Forgiveness." Nature 355:206-207. Recent computer tournament results suggest that natural selection can favor reciprocal altruism in the form of TFT strategies. Reports the results from an article by M. Nowak and K. Sigmund in which they found that TFT facilitates the emergence of cooperation in a population of selfish players. When TFT strategies were not included in the population, selfish strategies prevail and cooperation does not evolve. Bower repeats Godfray's suggestion that evolution may favor simple rules and the cooperation may evolve more easily in nature where players interact with known others regularly. - abstract by LD Population dynamics - ESS/Population structure - clustering/Population structure - spatial models/Simulation.
• 19. Boyd, Robert. 1992. "The Evolution of Reciprocity when Conditions Vary." In Alliance Formation among Male Baboons: Shopping for Profitable Partners, edited by Alexander H. Harcourt and Frans B.M. de Waal, pp. 473-489. Oxford: Oxford University Press.
  • Reviews work on reciprocal cooperation using the PD paradigm and suggests that some of this work makes unrealistic assumptions. Boyd presents and analyzes three variants of the PD in which game conditions vary. In each case, there is a range for which the basic results of Axelrod's and others' work remains unchanged, but for some parameter ranges altering these assumptions affects the evolutionary selection and stability of TFT-like strategies. The first model allows payoffs to vary among individuals. Boyd finds that selection may favor strategies that result in in a system of unbalanced reciprocity. In the case where payoffs vary among interactions, a wide range of strategies may be ESS. Finally, if the expected number of interactions is allowed to vary, suspicious strategies that delay the initiation of cooperation may be favored. Boyd concludes by noting that "the fact that distinctive reciprocating strategies are favoured in different circumstances may provide an avenue for empirical detection of reciprocity using the comparative method" (p. 487). - abstract by LD Payoffs - comparing different PD matrices/Population dynamics/Population structure/Limited set of allowable rules - enumerated set/Deductive
• 20. Boyd, Robert. 1988. "Is the Repeated Prisoner's Dilemma a Good Model of Reciprocal Altruism?" Ethology and Sociobiology 9:211-222.
  • Axelrod and Hamilton (1981) used the repeated prisoner's dilemma game as a basis for their widely cited analysis of the evolution of reciprocal altruism. Recently, it has been argued that the repeated prisoner's dilemma is not a good model for this task. Some critics have argued that the single period prisoner's dilemma represents mutualistic rather than altruistic social interactions. Others have argued that reciprocal altruism requires that the opportunities for altruism occur sequentially, first one individual and then after some delay the other. Here [Boyd] begin[s] by arguing that the single period prisoner's dilemma game is consistent with the definition of altruism that is widely accepted in evolutionary biology. Then [Boyd] present[s] two modified version of the repeated prisoner's dilemma, one in which behavior is sequential, and a second in which behavior occurs in continuous time. Each of these models shares the essential qualitative properties with the version used by Axelrod and Hamilton. Payoffs - comparing different PD matrices/Population dynamics - ESS/Population structure/Limited set of allowable rules - enumerated set/Theory/Deductive.
• 21. Boyd, Robert. 1989. "Mistakes Allow Evolutionary Stability in the Repeated Prisoner's Dilemma Game." Journal of Theoretical Biology 136:47-56.
  • The repeated prisoner's dilemma game has been widely used in analyses of the evolution of reciprocal altruism. Recently it was shown that no pure strategy could be evolutionarily stable in the repeated prisoner's dilemma. Here [Boyd] show[s] that if there is always some probability that individuals will make a mistake, then a pure strategy can be evolutionarily stable provided that it is "strong perfect equilibria" against itself. To be a strong perfect equilibrium against itself, a strategy must be the best response to itself after every possible sequence of behavior. [Boyd] show[s] that both unconditional defection and a modified version of tit-for-tat have this property. Noise - misimplementation/Population dynamics - ESS/Population dynamics - replicator dynamics/Theory/Deductive.
• 22. Boyd, Robert and Peter J. Richerson. 1990. "Culture and Cooperation." In Beyond Self-Interest, edited by Jane J. Mansbridge, pp. 111-132. Chicago: University of Chicago Press.
  • Examines the question of why human, unlike other mammals, cooperate in large groups of unrelated individuals. Kinship and reciprocity explain cooperation in small groups, but not large. Boyd and Richerson suggest one possible solution to this puzzle is that of cultural selection. In order for an explanation of cultural selection to work, there needs to be some mechanism which maintains cultural differences and variation, or otherwise populations of defectors would spread more quickly than those of cooperators. A theory of cultural selection must also describe the social or psychological mechanisms at work that could counter influences at the level of individual genes. Boyd and Richerson construct a simple model of group selection with four basic processes: enculteration, individual learning, the flow of ideas in society, and the extinction of societies. Using this model, defectors spread quickly and cooperation exists only among small groups. They add a fifth factor to the model, conformist cultural transmission, in which children acquire disproportionately the more common adult trait. With the addition of this process, the authors find that groups of cooperators can be selected. The authors briefly draw out some of the implications of their findings, including those for the kinds of trait transmitted, conformist traditions versus individual learning, and ethnic cooperation and conflict. - abstract by LD Interactions/Population structure - clustering/Population size/Sociology and anthropology/Theory
• 23. Boyd, Robert and Peter J. Richerson. 1988. "The Evolution of Reciprocity in Sizable Groups." Journal of Theoretical Biology 132:337-356.
  • Recently, several authors have investigated the evolution of reciprocal altruism using the repeated prisoner's dilemma game. These models suggest that natural selection is likely to favor behavioral strategies leading to reciprocal cooperation when pairs of individuals interact repeatedly in potentially cooperative situations. Using the repeated n-person prisoner's dilemma game, [the authors] consider whether reciprocal altruism is also likely to evolve when social interactions involve more individuals. [The authors] show that the conditions that allow the evolution of reciprocal cooperation become extremely restrictive as group size increases. Interactions/Population dynamics - ESS/Population structure/Theory/Deductive.
• 24. Boyd, Robert and Peter J. Richerson. 1989. "The Evolution of Indirect Reciprocity." Social Networks 11:213-236.
  • Human societies are based on cooperation among large numbers of genetically unrelated individuals. This behavior is puzzling from an evolutionary perspective. Because cooperators are unrelated it cannot be the result of kin selection, and the large scale seems to preclude explanations based on direct reciprocity. Alexander (1987) has proposed that large-scale cooperation among humans can be understood as resulting from networks of "indirect" reciprocity. For example, individual A may help individual B even though A receives no direct reciprocal benefit. Instead, B might help C who helps D who finally returns the help indirectly to A. Here [Boyd and Richerson] describe a simple mathematical model of the evolution of indirect reciprocity. Analysis of this model suggests that indirect reciprocity is unlikely to be important unless interacting groups are fairly small. Limited set of allowable rules - enumerated set/Theory/Deductive.
• 25. Boyd, Robert and Peter J. Richerson. 1990. "Group Selection among Alternative Evolutionarily Stable Strategies." Journal of Theoretical Biology 145:331-342.
  • Many important models of the evolution of social behavior have more than one evolutionarily stable strategy (ESS). Examples include co-ordination games, contests, mutualism, reciprocity, and sexual selection. Here [the authors] show that when there are multiple evolutionarily stable strategies, selection among groups can cause the spread of a strategy that has the lowest extinction rate or highest probability of contributing to the colonization of empty habitats, and that this may occur even when groups are usually very large, migration rates are substantial, and "extinction" entails only the disruption of the group and the dispersal of its members. The main requirements are: (1) individuals drawn from a single suriving group make up a sufficiently large fraction [of] newly formed groups, and (2) the processes increasing the frequency of successful strategies within groups are strong compared to rate of migration among groups. The latter condition suggests that this form of group selection will be particularly important when behavioral variation is culturally acquired. Population dynamics - ESS/Population structure/Sociology and anthropology/Theory/Deductive.
• 26. Boyd, Robert and Peter J. Richerson. 1992. "Punishment Allows the Evolution of Cooperation (or Anything Else) in Sizable Groups." Ethology and Sociobiology 13:171-195.
  • Existing models suggest that reciprocity is unlikely to evolve in large groups as a result of natural selection. In these models, reciprocators punish noncooperation by withholding future cooperation, and thus also penalize other cooperators in the group. Here, [the authors] analyze a model in which the response is some form of punishment that is directed solely at noncooperators. [Boyd and Richerson] refer to such alternative forms of punishment as retribution. [They] show that cooperation reinforced by retribution can lead to the evolution of cooperation in two qualitatively different ways. (1) If benefits of cooperation to an individual are greater than the costs to a single individual of coercing the other n - 1 individuals to cooperate, then strategies which cooperate and punish noncooperators, strategies which cooperate only if punished, and, sometimes, strategies which cooperate but do not punish will coexist in the long run. (2) If the costs of being punished are large enough, moralistic strategies which cooperate, punish noncooperators, and punish those who do not punish noncooperators can be evolutionarily stable. [Boyd and Richerson] also show, however, that moralistic strategies can cause any individually costly behavior to be evolutionarily stable, whether or not it creates a group benefit. Interactions/Noise - misimplementation/Endogenous ending/Population dynamics - ESS/Population size/Theory/Deductive/Sociology and anthropology.
• 27. Brelis, Matthew. 1992. "Reputed Mobster Defends His Honor." Boston Globe, 18 March, section 1:23.
  • The story of a reputed mobster, Vincent Ferrara, who called the Boston Globe because he was concerned about a story that had appeared in the paper that reported that he would testify against a mob boss. Ferrara said that he had not agreed to testify, and that the story the paper had run threatened the reputation he had earned for himself by making him look like an informant. He also said that such a story might prove harmful to him in the future. The situation resembles the story of the PD with a twist: here the prisoner wants to cooperate in order to maintain his reputation (and his health). - abstract by LD Interactions/Payoffs/Reputation/Politics and law - domestic/Miscellaneous.
• 28. Browne, Malcolm W. 1988. "Some Thoughts on Self-Sacrifice." New York Times, 5 July, 24.
  • Considers situations in nature in which organisms sacrifice themselves for the good of the community. Discusses a study that looked at sperm cells in rats and found that up to fifty percent of the cells were deformed. The researchers suggested that the deformities might serve some biological purpose. They found that after healthy sperm cells enter the reproductive tract of a female rat, the deformed sperm mass together, form a plug, and die, thereby preventing other sperm form fertilizing the egg and guaranteeing "genetic victory" to one of the first arrivals. Browne suggests that this is an example of social cooperation, and considers other examples of self sacrifice for community good, including runt tadpoles that do not compete with better developed siblings for nutrients, but do compete with non-siblings. - abstract by LD Biological applications.
• 29. Bull, J.J. and W.R. Rice. 1991. "Distinguishing Mechanisms for the Evolution of Co-operation." Journal of Theoretical Biology 149:63-74.
  • The existence of co-operation between species has been cast as a problem to the selfish-gene view of evolution: why does co-operation persist, when it would seem that individual selection should favor the unco-operative individual who exploits the co-operative tendencies of its partner and gives nothing in return? The recent literature has emphasized one type of model as underlying the evolution and stability of interspecific co-operation, which [Bull and Rice] term the "partner-fidelity" model, and which is typified by the game theory model known as the iterated Prisoner's Dilemma game. Under this mechanism, individuals are associated with the same partner(s) during an indefinite sequence of interactions. Individuals who at any time fail to co-operate with their partner can be penalized by those same partners in subsequent trials, hence the co-operation can be evolutionarily stable. Many examples of biological co-operation that have been offered appear to conform to this model. However, a few examples appear instead to fit a different and unrecognized mechanism, termed "partner-choice". Under partner-choice, individuals are associated for just one interaction, but an asymmetry enables one member to differentially reward co-operative vs. unco-operative partners in advance of any possible exploitation. Possible examples of co-operation maintained through partner-choice mechanisms are provided by the yucca/yucca moth system and the fig/fig wasp system. Population structure - information requirements/Biological applications/Theory.
• 30. Bunn, George and Rodger A. Payne. 1988. "Tit-for-tat and the Negotiation of Nuclear Arms Control." Arms Control 9:207-233.
  • Discussion of the advantages and difficulties of applying TFT strategies to arms control negotiations. PD situations differ from two person negotiations in two ways: negotiations allow for communication, and there are many more choices or options available. In the PD, there is no communication between the players, and there are only two options, to cooperate or to defect. TFT like strategies could fit arms control negotiations for several reasons (for example, TFT models the action-reaction that precedes bargaining; empirical work suggests that TFT-like strategies describe the actual behavior of the superpowers). Ultimately, however, the authors argue that TFT is better as a means to initiate negotiations, rather than a model for them once they begin. In particular, it is difficult to meet the four characteristics of TFT in reality. First, clarity is difficult in a bargaining situation: there is some chance of misperception, the choices are not always clear, and different issue are often linked together. Second, being unilaterally nice may be dangerous to a country's national security. Third, reciprocity is difficult given real world time demands; for example, democracies may not be able to respond quickly, given the number of different actors involved in decision making (the public, the legislature, etc.). Finally, episodes of cheating are often highly publicized as a form of leverage in the negotiations process. Thus, there are several theoretical and practical difficulties in applying TFT strategies to arms control negotiations. However, the authors note two practical implications of their discussion: first, TFT strategies may be useful in getting negotiations started, and second, through communication in the bargaining process the PD may be transformed into a more cooperative game. - abstract by LD Politics and law - international.
• 31. Busch, Marc L. and Eric R. Reinhardt. 1993. "Nice Strategies in a World of Relative Gains: The Problem of Cooperation under Anarchy." Journal of Conflict Resolution 37:427-445.
  • The debate between neoliberals and realists in the field of international relations draws heavily on the findings offered in Robert Axelrod's Evolution of Cooperation. Axelrod's well-known argument is that cooperation can emerge among egoists despite the absence of a central authority. This article assesses the robustness of Axelrod's findings in light of the realist critique that relative gains concerns make cooperation less likely than neoliberals contend. [Busch and Reinhardt] build on an amended prisoner's dilemma (PD) game and conduct a computer simulation tournament in which [they] vary (1) the payoff structure and (2) Axelrod's population of strategies. The results indicate that cooperation can emerge even under strong relative gains concerns, so long as the population of strategies is sufficiently retaliatory. On the basis of this finding, [the authors] argue that the realist critique is overstated: the introduction of greater relative gains concerns does not necessarily limit the prospects for cooperation among states. Payoffs - comparing different PD matrices/Relative vs. absolute gains/Politics and law - international/Simulation.
• 32. Buss, David M. 1991. "Evolutionary Personality Psychology." Annual Review of Psychology 42:459-91.
  • Describes the linkage between evolutionary psychology and personality psychology. Evolutionary theory has the potential to organize "seemingly arbitrary personality theories by anchoring a theory of human nature in processes known to govern all life. . . . Personality theories inconsistent with evolutionary theory stand little chance of being correct" (p. 461). There are three parts of evolutionary personality theory (pp. 476-477). First is the identification of adaptive problems faced by ancestral populations. Second, consider the relationship between current, observable personality factors and the proposed problems faced by ancestors. The theory must show how current personality features solve or solved these problems. Finally, the theory must explain individual differences in the adoption and use of behavioral strategies produced by these underlying psychological mechanisms. Buss uses an evolutionary perspective to re-frame the central questions and concerns of personality theory, including problems of consistency, interactionism, the role of context and environment, emotions, and culture. - abstract by LD Biological applications/Sociology and anthropology/Psychology/Theory/Collateral research.
• 33. Caporael, Linnda R., Robyn M. Dawes, John M. Orbell and Alphons J.C. van de Kragt. 1989. "Selfishness Examined: Cooperation in the Absence of Egoistic Incentives." Behavioral and Brain Sciences 12:683-739.
  • Social dilemmas occur when the pursuit of self-interest by individuals in a group leads to less than optimal collective outcomes for everyone in the group. A critical assumption in the human sciences is that people's choices in such dilemmas are individualistic, selfish, and rational. Hence, cooperation in the support of group welfare will only occur if there are selfish incentives that convert the social dilemma into a nondilemma. In recent years, inclusive fitness theories have lent weight to such traditional views of rational selfishness on Darwinian grounds. To show that cooperation is based on selfish incentives, however, one must provide evidence that people do not cooperate without such incentives. In a series of experimental social dilemmas, subjects were instructed to make single, anonymous choices about whether or not to contribute money for a shared "bonus" that would be provided only if enough other people in the group also contributed their money. Noncontributors cited selfish reasons for their choices; contributors did not. If people are allowed to engage in discussion, they will contribute resources at high rates, frequently on irrational grounds, to promote group welfare. These findings are consistent with previous research on ingroup biasing effects that cannot be explained by "economic man" or "selfish gene" theories. An alternative explanation is that sociality was a primary factor shaping the evolution of Homo sapiens. The cognitive and affective mechanisms underlying such choices evolved under selection pressures on small groups for developing and maintaining group membership and for predicting and controlling the behavior of other group members. This sociality hypothesis organized previously inexplicable and disparate phenomena in a Darwinian framework and makes novel predictions about human choice. Peer responses and commentaries follow. Interactions/Sociology and anthropology/Psychology/Empirical.
• 34. Carrasco, Enrique R. 1993. "Chile, Its Foreign Commercial Bank Creditors and Its Vulnerable Groups: An Assessment of the Cooperative Case-by-Case Approach to the Debt Crisis." Law and Policy in International Business 24:273-389.
  • Uses game theory to consider the question of why the cooperative case-by-case approach to the Latin American debt crisis was successful. Chile was the first Latin American country to adopt a highly cooperative approach to dealing with its debt problems: it made an effort to meet its obligations, and in return expected creditors to help restructure debt and re-establish access to the voluntary lending market and economic growth. Carrasco argues that the Latin American debtors and their creditors faced a negotiator's dilemma, a form of the PD, since cooperative approaches created value through cooperative ventures for both debtors and creditors, but simply competition to claim value or success did not substantively aid either party. Carrasco suggests that the case-by-case approach implicitly heeds Axelrod's advice not to defect first, to reciprocate, and not to be too clever. Relative to other Latin American countries, Chile's efforts with this cooperative approach yielded debt reduction and economic growth. However, Carrasco argues that this cooperation between Chile and its creditors succeeded in part because it was subsidized by the most vulnerable groups in Chile (e.g., the poor), who suffered the most when the country attempted to meet its international financial commitments. The failure of the case-by-case approach was that it did not address the costs that cooperation imposed on the vulnerable. - abstract by LD Payoffs/Politics and law - international/Economics and business.
• 35. Ceccatto, H.A. and B.A. Huberman. 1989. "Persistence of Nonoptimal Strategies." Proceedings of the National Academy of Sciences, USA 86:3443-3446.
  • For other work on asynchronous choices, see B.A. Huberman and N.S. Glance (1993) "Evolutionary Games and Computer Simulations." PNAS, USA 90:7716-7718. For work that uses thermodynamic models to model cooperation, see N.S. Glance and B.A. Huberman (1994) "The Dynamics of Social Dilemmas." Scientific American 270:76-81. Metastable configurations in open computational systems with local minima in their optimality functions are shown to be very long lived, which makes them effectively stable. When rare transitions to the global optimum do occur, they happen extremely fast, in analogy to models of punctuated evolution in biology. These results are obtained by introducing a thermodynamic-like formalism that allows for a simple analysis of nonlinear game dynamics in computational systems. Interactions/Payoffs/Population dynamics - ESS/Population dynamics - replicator dynamics/Population structure/Theory/Deductive/Simulation/Collateral research.
• 36. Chagnon, Napoleon A. 1988. "Life Histories, Blood Revenge, and Warfare in a Tribal Population." Science 239:985-992.
  • The revenge pattern Chagnon discusses resembles TFT. Swift retaliation for offenses served as a deterrent over the long run; those who avenged kin deaths enjoyed greater reproductive success. - LD Blood revenge is one of the most commonly cited causes of violence and warfare in tribal societies, yet it is largely ignored in recent anthropological theories of primitive warfare. A theory of tribal violence is presented showing how homicide, revenge, kinship obligations, and warfare are linked and why reproductive variables must be included in explanations of tribal violence and warfare. Studies of the Yanomamo Indians of Amazonas during the past 23 years show that 44 percent of males estimated to be 25 or older have participated in the killing of someone, that approximately 30 percent of adult male dealths [sic] are due to violence, and that nearly 70 percent of all adults over an estimated 40 years of age have lost a close genetic relative due to violence. Demographic data indicate that men who have killed have more wives and offspring than men who have not killed. Sociology and anthropology/Empirical/Collateral research.
• 37. Coalitions and Alliances in Humans and Other Animals. 1992. Edited by Alexander H. Harcourt and Frans B.M. de Waal. Oxford: Oxford University Press.
  • An attempt to bring together important work on coalitions and alliances. Harcourt and de Waal distinguish between a coalition and alliance by stating that coalitions are one-time cooperative acts by one or more individuals against a third party, whereas alliances are ongoing cooperative relationships. Both coalitions and alliances can be seen as means of competition. The book is divided into three sections: coalitions, alliances and societal structure; cooperative strategies in the "political" arena; and evolutionary considerations. The individual chapters cover a wide range of topics and applications. Axelrod's work is cited in several of the chapters and introductions to the sections. - abstract by LD Interactions/Population structure/Biological applications/Sociology and anthropology/Politics and law - international/Psychology/Empirical.
• 38. Condlin, Robert J. 1992. "Bargaining in the Dark: The Normative Incoherence of Lawyer Dispute Bargaining Role." Maryland Law Review 51:1-104.
  • Considers the question of dispute settlements among lawyers. The situation resembles a PD in that lawyers promote their own interests by cooperating with each other, but ethical norms oblige lawyers to compete with each other and do their best to promote their clients' selfish goals. Condlin uses Axelrod's results and the PD to suggest that cooperative interactions are more likely when the parties believe that they will be involved in bargaining relationships in the future. He also notes that there are some problems with translating Axelrod's work into practice: the PD simplifies reality, and it is hard for one party to know what the other has done. Also, in contrast to their ethical obligations, Axelrod's analysis suggests that lawyers are better off in the long run by cooperating with each other. Condlin suggests that lawyers have developed stylized bargaining norms that allow them to signal their cooperativeness to other lawyers, but simultaneously to appear to defend their clients' interests zealously. Condlin concludes by considering some of the ways to resolve this dilemma: accept the system and do nothing; make cooperative bargaining more ethical; make ethical bargaining more practical for lawyers; or to rely on discretionary advocacy. - abstract by LD Norms/Politics and law - domestic.
• 39. Cooperation and Prosocial Behaviour. 1991. Edited by Robert A. Hinde and Jo Groebel. Cambridge: Cambridge University Press.
  • An edited volume which considers various aspects of cooperation. The primary topics include cooperation in animals and humans; the development of prosocial tendencies; the situational and personality determinants of prosocial behavior; trust, commitment, and cooperation; and cooperation between groups. Each section has a brief introductory editorial which serves as an overview or commentary on the topic. Axelrod is cited briefly in chapters 1, 2, and 15. - abstract by LD Population structure/Norms/Biological applications/Sociology and anthropology/Politics and law - domestic/Politics and law - international/Psychology.
• 40. Crawford, Vincent P. and Hans Haller. 1990. "Learning How to Cooperate: Optimal Play in Repeated Coordination Games." Econometrica 58:571-595.
  • This paper proposes a characterization of optimal strategies for playing certain repeated coordination games whose players have identical preferences. Players' optimal coordination strategies reflect their uncertainty about how their partners will respond to multiple-equilibrium problems; this uncertainty constrains the statistical relationships between their strategy choices players can bring about. [The authors] show that optimality is nevertheless consistent with subgame-perfect equilibrium. Examples are analyzed in which players use precedents as focal points to achieve and maintain coordination, and in which they play dominated strategies with positive probability in early stages in the hope of generating a useful precedent. Choices/Payoffs/Limited set of allowable rules - limited rationality/Theory/Deductive/Collateral research.
• 41. Dacey, Raymond and Norman Pendegraft. 1988. "The Optimality of Tit-For-Tat." International Interactions 15:45-64.
  • The paper examines the performance of tit-for-tat in iterated plays of prisoners' dilemma and chicken. In particular, the paper examines, via computer simulations, a space of surrogate Axelrod-type tournaments over these games. The surrogate tournaments are specified in terms of characteristics of strategies similar to those Axelrod identifies as fundamental. The paper shows that the zones of optimality for tit-for-tat in tournament play of both prisoners' dilemma and chicken remarkably constrained, but that tit-for-tat generally does well relative to other strategies. Furthermore, [the] results show that the success of tit-for-tat is sensitive to the number of players and the assignment of payoff values. Payoffs/Payoffs - comparing different PD matrices/Population size/Limited set of allowable rules - parameterized rules/Simulation.
• 42. Dawes, Robyn M., Alphons J.C. van de Kragt and John M. Orbell. 1990. "Cooperation for the Benefit of Us - Not Me, or My Conscience." In Beyond Self-Interest, edited by Jane J. Mansbridge, pp. 97-110. Chicago: University of Chicago Press.
  • Consider the class of social dilemmas, such as the PD, in which actions good for group members acting individually produce outcomes which are bad for the collective group. The authors note four ways to resolve such dilemmas, each of which relies on manipulating the consequences for the individual of cooperating or defecting: the Leviathan, reciprocal altruism and TFT from Axelrod's work, mutual coercion, and socially instilled consciences. Based on a series of experiments, the authors show that the rates of cooperation in the one-shot PD can be dramatically affected by group identity or solidarity, by allowing for discussion among subjects, even in the absence of factors such as reputation and future rewards and punishments. The authors conclude that "with no discussion, egoistic motives explain cooperation; with discussion, group identity - alone or in interaction with verbal promises - explains its dramatic increase" (p. 107). The authors also comment on methodology in previous experiments used to examine cooperation, particularly directions which instruct individuals to attend to relative gains or situations which examine only repeated interactions. - abstract by LD Interactions/Payoffs - comparing different PD matrices/Psychology/Empirical
• 43. Dawkins, Richard. 1989. The Selfish Gene: New Edition. Oxford: Oxford University Press.
  • New edition of the 1976 classic about the "gene's-eye view" of evolution. The original text of the book is unchanged in the new edition, although endnotes have been added to correct and update the original. There are also two new chapters. Chapter 12, "Nice Guys Finish First," draws heavily on Axelrod's work. Dawkins provides a relatively extensive description and discussion of Axelrod's book, including defining the PD, the importance of iteration, the round-robin tournaments, characteristics of successful strategies, the importance of environment, and the simulations. He considers how clusters might develop, especially through kinship. Dawkins shows how the PD might be applied to divorce situations, bacteria, fig wasps, sea bass and vampire bats, and he suggests that genes might have been unconsciously selected to play the PD as a rule of thumb. Chapter 13, "The Long Reach of the Gene," briefly discusses the question explored at length in Dawkins's book The Extended Phenotype. of why genes came together in large vehicles (such as individuals). - abstract by LD Population dynamics - ESS/Population structure - clustering/Biological applications/Sociology and anthropology/Theory.
• 44. Downs, George W. 1991. "Arms Races and War." In Behavior, Society, and Nuclear War, vol. 2, edited by Philip E. Tetlock, Jo L. Husbands, Robert Jervis, Paul C. Stern, and Charles Tilly, pp. 73-109. Oxford: Oxford University Press.
  • Examines the theoretical and methodological foundations of arms races and war, and the relationship between the two. No clear, reliable theory exists that describes the conditions or situations under which arms races lead to war. He reviews the empirical work on arms races, considering multiple case studies and aggregate analyses separately. Downs discusses some of the omissions and shortcomings in this work, and suggests that a theory which hopes to link arms races to war should include conditions under which deterrence can be sustained, the role of strategy among decision makers, and view changes in arms as a decision variable. He examines TFT as a possible prescription for decreasing the chances of arms races leading to war, because the arms balance is maintained. However, problems with using TFT arise when there is either an imbalance in resources or in arms between the two sides. Downs considers other aspects that should ideally be included in a theory linking arms races to war, including the challenges of the security dilemma and spiral theory, with the importance of misperception and their use of psychological theories. Ideally all of these factors should be incorporated into one model, although this integration is likely to be a gradual process. Downs reviews some work that has begun to address questions about misperception and the importance of understanding the assumptions that underlie various models. - abstract by LD Noise - misperception/Politics and law - international/Psychology
• 45. Druckman, Daniel and Benjamin J. Broome. 1991. "Value Differences and Conflict Resolution: Familiarity or Liking?" Journal of Conflict Resolution 35:571-593.
  • Effects of familiarity and liking on negotiating perceptions and behaviors are explored in two experiments, one focusing on prenegotiation expectations and perceptions (experiment 1), the other on negotiation processes and outcomes (experiment 2). Both experiments were embedded in the context of a simulation of conflict between groups resembling the Greek and Turkish communities in Cyprus. Results obtained in the two experiments showed different effects for the familiarity and liking variables: Analytically distinct effects for these variables on prenegotiation perceptions contrasted with the combined effects on negotiating behavior and postnegotiation perceptions. In experiment 1, liking influenced expected movement from initial positions, perceptions of the opponent, and types of strategies prepared for the negotiation; familiarity had its primary impact on perceptions of the situation as being conducive to agreement. Results of experiment 2 showed that reducing either liking or familiarity served to reduce willingness to reach compromise agreements, whether actual or desired. These results suggest that the positive effects obtained for a facilitation condition reported in an earlier study by Druckman, Broome, and Korper (1988) may have been due to the familiarity and liking produced by the experimental manipulation. Implications of the results obtained in both experiments are discussed in terms of changing expectations and uncertainty reduction. Further analyses of negotiating process dynamics would elucidate the difference between reaching agreements in the short run and developing relationships between groups over the long term. Politics and law - international/Psychology/Empirical/Collateral research.
• 46. Dugatkin, L.A. 1988. "Do Guppies Play TIT FOR TAT during Predator Inspection Visits?" Behavioral Ecology and Sociobiology 23:395-399.
  • Cooperative behavior during predator-inspection visits of the guppy (Poecilia reticulata) was examined. Wild caught guppies from Trinidad were tested on two types of mirror. In one treatment individual guppies were tested using a long mirror that ran parallel to the path toward the predator. In the second treatment, guppies were tested with a shorter mirror that was placed at an angle of thirty-two degrees to the path toward the predator. Guppies in both mirror treatments showed consistent behavior throughout a trial, with subjects in the straight-mirror treatment spending more time near the predator. It appears that guppies employ a "conditional-approach" strategy during predator inspections. The conditional-approach strategy instructs a player to swim toward the predator (inspect) on the first move of a game and subsequently only to move forward if the other player swims beside it. "Conditional-approach" is analogous to a TIT FOR TAT strategy, the difference being that the conditional-approach strategy makes no assumptions about the player's payoff matrix. Biological applications/Biological applications - specific species - fish.
• 47. Dugatkin, Lee Alan. 1992. "The Evolution of the "Con Artist"." Ethology and Sociobiology 13:3-18.
  • A series of game-theoretical models for the evolution of, what in the folk literature has become known as, the "Confidence Artist" is presented. Con artists are assumed to be noncooperators who move between groups and "prey" on naive cooperators. Cooperators learn about con artists by either direct experience or via cultural transmission about the identity (or behavior) of such individuals. Three types of transmission rules about con artists are modeled: 1) transmission rate that is independent of the frequency of con artists in the metapopulation; 2) transmission such that cooperators, with some probability, can learn about particular con artists who have entered their group; and 3) a type of frequency dependent transmission such that cooperators can identify con artists in proportion to their frequency in the metapopulation. In general, cultural transmission works against con artists by 1) decreasing the critical between travel patch travel time to invade a metapopulation of cooperators or 2) decreasing the equilibrial frequency of con artists (compared to the case of no cultural transmission). Depending on the mode of cultural transmission, con artists may exist at relatively high or low frequencies. Population structure - information requirements/Limited set of allowable rules - enumerated set/Biological applications/Sociology and anthropology/Simulation.
• 48. Dugatkin, Lee Alan. 1990. "N-person Games and the Evolution of Co-operation: A Model Based on Predator Inspection in Fish." Journal of Theoretical Biology 142:123-135.
  • Considers the potential importance of the relationship between population size and cooperative behavior. Dugatkin finds that cooperation may invade large populations more easily than smaller ones, but it is likely to represent a smaller proportion of the population in larger groups. - LD Two N-person game theoretical models examining the evolution of co-operation during predator inspection in fish are presented. Predator inspection occurs in small shoals of fish, in which one to a few individuals, the "inspectors" (co-operators) break away from the shoal and cautiously approach a predator to obtain information on this potential danger. In the models presented here, remaining with the shoal and not inspecting is considered an act of defection. Both model I and II produce a stable internal polymorphism of inspectors and noninspectors. While the equilibrial frequency of inspectors can be low (i.e. <10%) at large shoal size, the proportion of shoals containing any inspectors - and therefore exhibiting the inspection behavior - is much greater. Both models presented here, and N-person games in general are equivalent to intrademic group selection models of evolution in structured populations, in which shoals are trait groups and co-operation evolves by between-shoal selection. While the results are cast in terms of predator inspection, the model itself is general and applies to any multi-group scenario where co-operators benefit entire groups at their own expense. The results presented here add to the mounting theoretical and empirical evidence that co-operation is frequently not a pure evolutionarily stable strategy, and that many metapopulations should be polymorphic for both co-operators and defectors. Interactions/Payoffs/Population dynamics - ESS/Population structure/Biological applications/Simulation.
• 49. Dugatkin, Lee Alan and David Sloan Wilson. 1991. "Rover: A Strategy for Exploiting Cooperators in a Patchy Environment." American Naturalist 138:687-701.
  • [Dugatkin and Wilson] present a computer simulation that examines the dynamics of cooperative behavior in a patchy environment. A new defecting strategy called "ROVER" is introduced, which uses a rule analogous to the "marginal value" theorem to determine how long to stay in a patch. A wide range of parameter values allow ROVERs to invade a metapopulation of tit-for-tat strategists (TFT) and spread either to fixation or to a stable equilibrium in which ROVER is the majority strategy. [The] model, along with previous models that invoke different mechanisms, suggests that even guarded forms of cooperation such as TFT are often vulnerable to invasion and that a stable mixture of cooperators and exploiters might be common in nature. Choices/Payoffs - comparing different PD matrices/Population dynamics - ESS/Population structure - information requirements/Limited set of allowable rules - enumerated set/Theory/Simulation.
• 50. Evangelista, Matthew. 1990. "Cooperation Theory and Disarmament Negotiations in the 1950s." World Politics 42:502-528.
  • Evaluates theories of the sources of cooperation in international politics by looking at the 1955 case of U.S.-Soviet disarmament negotiations. The 1955 case is a specific instance of a more general question about why two sides fail to reach a cooperative outcome, even when both sides ostensibly agree on the terms. Evangelista briefly reviews theories of cooperation in PD situations and the case of Deadlock; both games have been used to characterize arms race situations. By examining the motivations of each side in the 1955 negotiations, Evangelista concludes that the situation resembled Deadlock and not the PD because only one side, the Soviets, was interested in the cooperative solution and saw the situation as a PD. The U.S. was not interested in disarming and thus did not view the situation as a PD. This illustrates Evangelista's argument about how a state's preferences may affect the type of game each plays. He concludes by drawing some parallels between 1955 and U.S.-Soviet negotiations in the late 1980s, and suggests that future work might try to link particular games to the "domestic political determinants of foreign policy" (p. 528). - abstract by LD Payoffs/Relative vs. absolute gains/Politics and law - international/Empirical.
• 51. Evangelista, Matthew. 1991. "Sources of Moderation in Soviet Security Policy." In Behavior, Society, and Nuclear War, vol. 2, edited by Philip E. Tetlock, Jo L. Husbands, Robert Jervis, Paul C. Stern, and Charles Tilly, pp. 254-354. Oxford: Oxford University Press.
  • Examines the basic question of the sources of change in Soviet security policy. Reviews academic and popular press theories of policy change, suggests the kinds of evidence that may be needed to test various theories, presents hypotheses for future work, and considers some promising methodological approaches. One of the seven academic theories discussed is cooperation theory, which draws heavily on Axelrod's presentation of TFT reciprocity. Evangelista notes that there may be problems with using the PD and TFT as models, particularly given the possibilities for misperception and the assumption of fixed preferences. He provides a substantial overview of evidence from the Soviet case, from Khrushchev through Gorbachev, that might be useful for testing some of these theories. The Limited Test Ban Treaty of 1963 is presented as an example where TFT and a PD model might explain changes in Soviet policy (pp. 296-302). Evangelista concludes by listing some hypotheses that might be tested empirically, using both comparative case studies and quantitative and statistical methods. - abstract by LD Payoffs/Politics and law - international
• 52. "Evo-Economics: Biology Meets the Dismal Science." 1994. Economist. 329:93-95.
  • Discussion of the emergence of evolutionary economics, grounded in the common interest of economics and evolution in the individual. Evolutionary economics blends the PD of economists (where individual self-interest leads to collective disaster) with the iterated PD of biologists (where cooperation may evolve in repeated play). TFT or reciprocal altruism may help economists to explain incidents of altruism and puzzles like the voter's paradox. However, even this explanation of altruism may be too narrow: TFT suggests that the payoffs or exchanges are in the same currency, but it may be that the payoffs are genetic, not economic. Beyond this, there are two primary differences between economics and evolutionists. Economists take consumption as an end in itself and take preferences as given. In contrast, evolutionists see consumption as a means to successful reproduction and develop theories to explain preferences. - abstract by LD Population structure - information requirements/Economics and business.
• 53. Farrell, Joseph and Roger Ware. 1989. "Evolutionary Stability in the Repeated Prisoner's Dilemma." Theoretical Population Biology 36:161-166.
  • Farrell and Ware suggest that future work might direct attention to mixtures of strategies and mutants that empirical observations suggest occur in the real world. - LD See also Louis Marinoff (1990) "The Inapplicability of Evolutionarily Stable Strategy to the Prisoner's Dilemma." Philosophy of Science 41:461-472. Recently, biologists have explored evolutionary explanations of apparently altruistic behavior in situations of conflict, often modeled as the "Prisoner's Dilemma." Certain simple cooperative strategies, notably TIT-FOR-TAT, have been successful in computer simulations of the evolution of populations of individuals who interact according to the Prisoner's Dilemma. Some attempts to formalize this have used the concept of "evolutionary stability." But Boyd and Lorberbaum (1987, Nature (London) 327, 58-59) recently showed that no single pure strategy (such as TIT-FOR-TAT) can be evolutionarily stable. [Farrell and Ware] extend [Boyd and Lorberbaum's] argument to derive a more powerful result, which implies, first, that no finite mixture of pure strategies can be evolutionarily stable, and, second, that no mixture of TIT-FOR-n-TATS can be evolutionarily stable. [Farrell and Ware] interpret [their] negative results to suggest that evolutionary stability is too demanding a criterion. Population dynamics - ESS/Theory/Deductive.
• 54. Fogel, David B. 1993. "Evolving Behaviors in the Iterated Prisoner's Dilemma." Evolutionary Computation 1:77-97.
  • Evolutionary programming experiments are conducted to investigate the conditions that promote the evolution of cooperative behavior in the iterated prisoner's dilemma. A population of logical stimulus-response devices is maintained over successive generations with selection based on individual fitness. The reward for selfish behavior is varied across a series of trials. Simulations indicate three distinct patterns of behaviors in which mutual cooperation in inevitable, improbable, or apparently random. The ultimate behavior can be reliably predicted by examining the payoff matrix that defines the reward for alternative joint behaviors. Payoffs - comparing different PD matrices/Population dynamics - ESS/Automata theory/Simulation.
• 55. "Forgiveness Math." 1993, May. Discover. 14:62-67.
  • Considers the question of how and why altruistic behavior came to exist in nature. Describes the PD and the importance of iteration to bringing about cooperative outcomes. Discusses the Axelrod tournaments and the success of Rapoport's TFT, and the result from Axelrod's simulations that TFT does best within a cluster of kin, but that it is also vulnerable to noise or errors. The author talks to Karl Sigmund about his simulation work with Martin Nowak. In a series of simulations with stochastic strategies, they found that including TFT in the population was important for ultimately bringing about a more cooperative population where Generous TFT (TFT, except when faced with defection by the other player, cooperate one out of every three times) was firmly established. Sigmund suggests that his future work will focus on trying to introduce longer memory into play to simulate the importance of trust in repeated interactions. - abstract by LD Population dynamics/Limited set of allowable rules/Theory/Miscellaneous.
• 56. Frank, Robert H. 1988. Passions within Reason: The Strategic Role of the Emotions. New York: W.W. Norton & Company.
  • Considers the class of commitment problems, one form of which is embodied in the PD. Commitment problems are ones in which "it is in a person's interest to make a binding commitment to behave in a way that will later seem contrary to self-interest," at least in the short run (p. 47). Frank says that materially self-interested or rational motives are important for understanding behavior, but that such models are ultimately inadequate for explaining behavior, and actions intended to maximize self-interest may fail to do so because the actors do not resolve their commitment problems. In Chapter 2, Frank notes the result from Axelrod that stable cooperation tends to emerge when there is a set of players who interact repeatedly and who are able to identify other cooperators. However, he suggests that Axelrod's work more closely parallels Darwinian individual selection as an explanation for the emergence of cooperation, and he turns to expanding upon Trivers's notion of the role of mediating emotions in engendering cooperation. Frank says that certain emotions, such as anger or guilt, which he calls moral sentiments, and the development of reputation, are mechanisms through which people can signal to others their willingness to cooperate in PD-like situations. Moral sentiments alter the material incentives that people face when making decisions, whereas reputation is a mechanism through which people can identify other cooperators. Neither mechanism is a perfect signal. Frank draws support for his arguments from various examples in the popular press, experimental data, and working through a formal version of the commitment model. - abstract by LD Interactions/Payoffs/Noise - misperception/Population structure - information requirements/Reputation/Economics and business/Sociology and anthropology/Psychology/Theory/Deductive/Empirical.
• 57. Frank, Robert. 1990. "A Theory of Moral Sentiments." In Beyond Self-Interest, edited by Jane J. Mansbridge, pp. 71-96. Chicago: University of Chicago Press.
  • Considers the question of how people keep commitments, and the incentives they have to fulfill promises. Frank says that specific emotions act as commitment devices. Some emotions, which he calls moral sentiments, compete with feelings that arise from rational calculations based upon material payoffs. These emotions, like guilt, alter people's incentives in ways such that people feel aversion to cheating, for example. Frank examines the role of moral sentiments in the context of the cheating problem in the PD, with attention to the importance of being able to recognize and to cooperate with other cooperators. Varying the cooperators' ability to recognize other cooperators, Frank suggests that the self-interested person might want to acquire moral sentiments, because such emotions can be used to help identify other potential cooperators. - abstract by LD Population structure - information requirements/Sociology and anthropology/Psychology/Theory/Deductive/Collateral research
• 58. Friedland, Nehemia. 1990. "Attribution of Control as a Determinant of Cooperation in Exchange Interactions." Journal of Applied Social Psychology 20:303-320.
  • Parties to conflict and to exchange interactions typically experience a considerable uncertainty as to the intentions and strategic plans of their adversaries. Such uncertainty is threatening and can therefore elicit competitive responses. Perceived control over an adversary's actions and over the course of an interaction can reduce uncertainty, lower the perceived risk of exploitation, and thus facilitate cooperative responses. This mediating role of perceived control was demonstrated in two experiments. They showed that certain patterns of change in one party's strategy enhanced the other party's perception of control and, concurrently, increased the frequency of its cooperative responses. A third experiment showed that variations in perceived control affect the tendency to cooperate, even if such variations are not directly related to or induced by the adversary's strategy. Psychology/Empirical.
• 59. Fudenberg, Drew and Eric Maskin. 1990. "Evolution and Cooperation in Noisy Repeated Games." American Economic Review 80:274-279.
  • Paper provides support for the intuition that efficient outcomes are more likely in repeated games. Repeated play in games like the PD can lead to cooperation, but there is a small chance that players in these games make mistakes, that their actions are not what they intended. Using an evolutionary simulation which randomly paired strategies against each other, and looking at symmetric two-player games (here, the PD and Battle of the Sexes), the authors found that if there is some small chance for misimplementation, evolution may weed out strategies that impose large penalties for deviations. If the penalties for deviation are not too drastic, then inefficient strategies can be invaded by efficient ones. If "there is a unique payoff pair that maximizes the sum of players' payoffs, then any ES (pure) strategy must be efficient. If there are multiple pairs that maximize the sum of the payoffs, then ES does not imply efficiency but still imposes restrictions on the set of equilibrium payoffs" (p. 275). Allowing only finitely complex strategies, they found that "any finitely complex ES strategy must give rise to the cooperative outcome in repeated games" (p. 278). If one allows infinitely complex strategies, then by the Folk Theorem ESS does not restrict possible payoffs. - abstract by LD Payoffs/Noise - misimplementation/Population dynamics - ESS/Population dynamics - replicator dynamics/Limited set of allowable rules - finite state machines/Theory/Simulation.
• 60. Getty, Thomas. 1987. "Dear Enemies and the Prisoner's Dilemma: Why Should Territorial Neighbors Form Defensive Coalitions?" American Zoology 27:327-336.
  • Game-theoretic arguments are used to derive two new hypotheses to explain why territorial residents so consistently defeat potential usurpers. Both hypotheses are based on help from established, familiar neighbors. The first hypothesis follows simply from Krebs' (1982) assertion that the value of a territory to a usurper must be decremented by the costs of negotiating dear-enemy relationships with the remaining neighbors. An implication is that the remaining neighbors will also have to pay these renegotiation costs if the usurper succeeds. The first hypothesis is that it may benefit a territorial animal to help its established neighbors defend so it can avoid having to renegotiate territorial boundaries with a new, unfamiliar neighbor. This hypothesis assumes net positive benefits for helping without requiring reciprocation. The second hypothesis requires reciprocation to compensate for immediate net costs of helping. An animal should help its neighbors fight off usurpers only if the neighbors will reciprocate. This hypothesis is based on the prisoner's dilemma game and builds on Axelrod's (1984) work. Cooperative defense (reciprocal help) can be an evolutionarily stable strategy (ESS) if several conditions are met. One critical condition is that the relationship between neighbors is relatively stable. Cooperative defense should help established neighbors retain their territories, and should therefore be a cause, as well as a consequence of stability. It is suggested that the necessary conditions are not very restrictive, that they are often met in nature, and that shared defense is observed but not recognized as such. Interactions/Population dynamics - ESS/Population structure - spatial models/Biological applications.
• 61. Glance, Natalie S. and Bernardo A. Huberman. 1994, March. "The Dynamics of Social Dilemmas." Scientific American 270:76-81.
  • Discussion of how to achieve cooperation in groups of various sizes in the context of an n-person PD game. Past work suggests that cooperation is more likely in smaller groups than in larger ones, and there is greater cooperation when players are allowed more communication with each other. Using computer simulations of the social behavior of groups drawn from theories from statistical thermodynamics, the authors examined the dynamics and the outcomes of group interactions. They found that there were two stable points in large groups: either there was a great deal or very little cooperation, with small fluctuations around these stable points, due to uncertainty within the group about the length of the game and about the effect of individual contributions on the group. Large random fluctuations were related to group size, which explained why the behavior of groups tended to be stable over time, but when it did change, why it changed quickly. The authors also considered the effects of introducing greater group diversity, and the evolution of cooperation in hierarchies. - abstract by LD Interactions/Payoffs/Population structure/Population size/Simulation.
• 62. Godfray, H.C.J. 1992. "The Evolution of Forgiveness." Nature 355:206-207.
  • Although repeated interactions may lead to reciprocal altruism, how does one account for the spread of such behavior in non-altruistic populations. In a PD, what is an individual's best response, based on previous interactions with the other animal? One solution, TFT, was proposed through Axelrod's work and tournaments, but this solution does not account for things like recognition errors. Another possible solution is Generous TFT (GTFT). GTFT responds to past cooperation with cooperation, but forgives defection on a certain proportion of the other player's defections. If the proportion of forgiveness is one-third, GTFT cannot be invaded by other GTFTs with different probabilities of forgiveness. Godfray considered whether GTFT could invade other populations by running a simulation. Against a population of Always Defect, GTFT cannot invade. However, if a population of Always Defect is first invaded by TFT, then GTFT can invade TFT. Godfray notes three implications for reciprocal altruism in nature. First, natural selection may favor simple rules, such as GTFT. Second, these rules are probabilistic and likely to be more forgiving than TFT. Finally, reciprocation strategies may invade more easily if there is an initial high probability of interactions between relatives. - abstract by LD Population dynamics - ESS/Population structure - clustering/Biological applications/Simulation.
• 63. Goldstein, Joshua S. 1991. "Reciprocity in Superpower Relations: An Empirical Analysis." International Studies Quarterly 35:195-209.
  • Past empirical studies of superpower reciprocity have produced inconsistent results that may be traced to several recurrent methodological problems. Correcting these problems, [Goldstein] analyzed statistically the responses of the United States and the Soviet Union to each other's actions over the past forty years. Results were replicated across quasi-experiments using different data sources, time periods, and model specifications. Both superpowers reciprocate each other's actions within a short time frame of up to about two months. Neither responds inversely (for example, by becoming more cooperative following hostile actions by the other). In the 1950s and 1960s U.S. reciprocity following Soviet actions was much more consistent than Soviet reciprocity following U.S. actions, but in the 1970s and 1980s Soviet reciprocity was more consistent than U.S. reciprocity. Noise/Politics and law - international/Empirical.
• 64. Goldstein, Joshua S. and John R. Freeman. 1990. Three-Way Street: Strategic Reciprocity in World Politics. Chicago: University of Chicago Press.
  • Discussion of cooperation and the relationship among the United States, the Soviet Union, and China. Using theories drawn from game theory and psychology in conjunction with data analysis and case studies, Goldstein and Freeman find a norm of bilateral reciprocity, and that cooperative acts elicit cooperation. However, hostile initiatives used to bring about cooperation usually fail, instead drawing hostile responses. Chapter 1 describes and critiques different theories of cooperation from game theory, psychology, and quantitative-empirical theory. The discussion of game theoretic approaches to cooperation draws heavily and extensively on Axelrod's work and the success of TFT. The authors draw four cooperative-reciprocal strategies from these theories to test against the data: TFT and three versions of GRIT (Graduated Reciprocation In Tension-reduction) from psychological theories. Chapter 2 sketches relationships among the three powers from 1948 through 1987; Chapter 3 provides the results of data analysis. Chapter 4 presents six case studies of cooperative initiatives. Chapter 5 evaluates the different cooperative-reciprocal strategies based on the evidence and simulation results. TFT was the least effective strategy, although the cooperative effects of all four of the strategies die out. Goldstein and Freeman suggest that this may be due to two-way reciprocity, and that one country's willingness to initiate cooperation may not be enough to promote cooperation among all three countries. The situation might better be seen as three linked dyadic games, rather than a three-person game, or a three-person game with payoffs such that triangular asymmetry makes sense for two of the players. Game theory has little to say about the latter situation, although rational expectations theory with Bayesian players in sequential games may be useful to explore in the future. - abstract by LD Interactions/Payoffs/Limited set of allowable rules - enumerated set/Politics and law - international/Empirical/Simulation.
• 65. Grieco, Joseph M. 1988. "Anarchy and the Limits of Cooperation: A Realist Critique of the Newest Liberal Institutionalism." International Organization 42:485-507.
  • The author provides a summary table of key differences between the theories he discusses on page 503. - LD Considers major theories in international relations, realism and liberal institutionalism. Neoliberal institutionalism is the most recent form of liberal institutionalism. Grieco hopes to show that "neoliberal institutionalism misconstrues the realist analysis of international anarchy and therefore it misunderstands the realist analysis of the impact of anarchy on the preferences and actions of states" (p. 487). Realists believe that anarchy in the international system leads to conflict, and that institutions are not capable of mitigating the effects of anarchy to bring about cooperation. Neoliberal institutionalists believe realists overstate the conflict within the system and the inability of institutions to engender cooperation. They suggest that there are countervailing forces, such as repeated interactions, pushing toward cooperation. Proponents of this theory are concerned with cheating as the major threat to cooperation; anarchy means that there is no organization to enforce rules against cheating. They identify the state's goal as to attain the greatest possible individual or absolute gain. Realists reject the concern with cheating; anarchy in the international system means that there is no way to prevent one state from using violence against another. Thus, realists believe that the state's goal is to ensure its survival and to worry about relative, not absolute, gains. Grieco concludes by suggesting that future work needs to conduct empirical tests of these two theories and briefly considers possible cases that might be used. - abstract by LD Politics and law - international/Relative vs. absolute gains.
• 66. Grieco, Joseph M. 1990. Cooperation among Nations: Europe, America, and Non-tariff Barriers to Trade. Ithaca, NY: Cornell University Press.
  • Explores the question of how and why states are willing to cooperate with each other given the constraints of anarchy. Grieco considers two competing theories of international relations, realism and neoliberal institutionalism, to determine which best explains the problem of international cooperation. In the first two chapters, he examines the logic of each theory and derives competing testable hypotheses from each. Chapters 3 through 7 are devoted to applying the two theories to explaining the case of the Toyko Round regime for the reduction of non-tariff barriers to trade. In the concluding chapter Grieco argues that realism is superior to neoliberal institutionalism in terms of its logic - the concerns with cheating and the gaps in relative gains - and its ability to explain political events. He suggests that future work should consider testing other core competing hypotheses from the two theories, such as the role of the shadow of the future and the partners states prefer in cooperative agreements. - abstract by LD Payoffs/Relative vs. absolute gains/Politics and law - international/Empirical.
• 67. Grieco, Joseph M. 1988. "Realist Theory and the Problem of International Cooperation: Analysis with an Amended Prisoner's Dilemma Model." Journal of Politics 50:600-624.
  • Realist political theory finds that states are positional in character. Thus, states prefer that relative achievements of jointly produced gains not advantage partners, and their concerns about relative gains may constrain their willingness to cooperate. Conventional presentations of the game of Prisoner's Dilemma do not depict Realism's specification of the relative gains element of the structure of state preferences or Realism's analysis of the capacity of state concerns about relative gains to impede cooperation. However, by distinguishing between game payoffs and state utility, an Amended Prisoner's Dilemma model can depict both the relative-gains element of state preferences and the relative-gains problem for cooperation. This Amended Prisoner's Dilemma facilitates analysis of an important systemic constraint on international cooperation identified by Realist political theory, contributes to our understanding of international institutions, and draws our attention to a number of potentially interesting research problems concerning international collaboration. Payoffs/Payoffs - comparing different PD matrices/Politics and law - international/Relative vs. absolute gains.
• 68. Hanson, David P. 1991. "Managing for Ethics: Some Implications of Research on the Prisoner's Dilemma Game." SAM Advanced Management Journal 56:16-20.
  • Considers the question of how managers can promote ethical conduct, behavior for the long-term good of the company, by applying some of the results from analyses of the PD. Drawing on Rapoport's and Axelrod's work, Hanson suggests that there are three conditions which make the PD more like reality and which promote cooperative or ethical outcomes: attention to the larger game and the actions of players other than one's partner; iteration; and retaliation against past defections. Under these conditions, Rapoport and Axelrod both found that TFT strategies were successful. Hanson notes that companies must face two levels of ethical decision making: within the industry marketplace, and within the company itself. Each firm has more control over the incentives for internal ethical decision making than it does over those in the marketplace. He considers the cases of pollution, defense contracting, and accounting. Legislation has effectively imposed the three Axelrod/Rapoport conditions in the case of pollution, but the incentives for the defense and accounting industries do not meet the three conditions for ethics in the marketplace. Hanson suggests that to meet the Axelrod/Rapoport conditions within the company, managers need to groom several applicants for each position so that no individual is indispensable (larger game), evaluate employees' long-term performances (iteration), and do not grant pardon for past misdeeds (retaliation for past defections). - abstract by LD Economics and business.
• 69. Harcourt, Alexander H. 1992. "Cooperation in Conflicts: Commonalities between Humans and Other Animals." Politics and the Life Sciences 11:251-259.
  • Examines similarities in the ways that humans and other animals cooperate in conflict situations. Harcourt argues that animal societies may be simpler analogues of human systems. He considers four questions: how does cooperation evolve and how is it maintained; when should a player ally with others; who are the best or preferred partners; and what is the influence of society on coalitions, and vice versa. Axelrod's work is used to describe how reciprocal altruism or TFT might explain the spread and maintenance of cooperation within a population. Harcourt draws on a number of zoological studies to support his arguments, and he concludes by noting that political science and zoology might learn a great deal from the other's work. - abstract by LD Biological applications/Population structure/Politics and law - domestic/Politics and law - international/Sociology and anthropology.
• 70. Harpending, Henry C. and Jay Sobus. 1987. "Sociopathy as an Adaptation." Ethology and Sociobiology 8:63S-72S.
  • Sociopathy in males and hysteria (Briquet's syndrome) in females very closely fit predictions from a model of characteristics of cheaters or nonreciprocators in a complex social system. Such a model is discussed and characteristics of sociopaths and hysterics are described. Since a successful cheating adaptation should require, above all else, concealment of the trait, recognition and diagnosis of these traits in humans will always be difficult and ambiguous at the level of language and interpersonal interaction. Population structure - information requirements/Limited set of allowable rules - limited rationality/Sociology and anthropology.
• 71. Harrington, John C. and Robert Axelrod. 1994. "Evolutionary Stability in the Iterated Prisoner's Dilemma with Noise." Under submission .
  • Argues that in a PD with noise due to misimplementation, pure ESSs, contrite TFT (CTFT) and Pavolv (win-stay, lose-shift), can exist, depending upon the discount rate and the payoffs. However, in a PD with noise due to misperception, there is no ESS. When the noise is a result of misimplementation, there is agreement between the players about what happened, so the players may be able to restore cooperation. When the noise is due to misperception, there is no agreement about what happened, so it may be more difficult to restore cooepraiton; Harrington and Axelrod suggest that future research should explore the restoration of cooperation with misperception. They conclude by noting that in order to understand the kinds of strategies that will evolve in a PD, it is important to know about the payoffs, the discount rate, and the type of noise. - abstract by LD Payoffs/Noise - misimplementation/Noise - misperception/Population dynamics - ESS/Limited set of allowable rules - enumerated set/Theory/Deductive.
• 72. Hart, Benjamin L. and Lynette A. Hart. 1992. "Reciprocal Allogrooming in Impala, Aepyceros melampus." Animal Behaviour 44:1073-83.
  • Adult female and male impala engage in a type of allogrooming in which partners alternately deliver bouts of oral grooming to the head and neck. These grooming encounters comprise typically six to 12 tit-for-tat-like exchanges of bouts and are highly reciprocal among adult females, adult bachelor males and subadult males. Although allogrooming among females could be between related individuals, that occurring among adult males would appear to be between unrelated individuals. Unlike allogrooming reported for some primate species and other ungulates, the dominant impala received no more grooming than the subordinate. It is proposed that one function of impala allogrooming is to reduce the ectoparasite load on body areas an animal cannot reach with its own mouth. The impala reciprocal allogrooming system is unique among free-ranging antelope and other ungulates and may be a candidate for the tit-for-tat strategy of evolved cooperation. Population dynamics - ESS/Biological applications/Biological applications - specific species - impala.
• 73. Hart, Lynette A. and Benjamin L. Hart. 1988. "Autogrooming and Social Grooming in Impala." Annals of the New York Academy of Sciences 525:399-402.
  • Compared the personal and social grooming habits of impala, Grant's gazelle, and common wildebeest. None of these animals can fully groom themselves, but because impala largely live in deciduous woodland areas, reciprocal social grooming should be particularly important for the removal of ticks. Observing female herds of the animals, the authors found that impala exhibited social oral grooming, whereas the gazelle and wildebeest did not. They suggest that reciprocal social grooming is a form of reciprocal altruism, not kin selection, since the females in these herds are unrelated. - abstract by LD Biological applications/Biological applications - specific species - impala/Collateral research.
• 74. Hauser, Marc D. 1992. "Costs of Deception: Cheaters Are Punished in Rhesus Monkeys (Macaca mulatta)." Proceedings of the National Academy of Sciences, USA 89:12137-12139.
  • From a functional perspective, deception can evolve in animal populations but should be constrained by the costs associated with detection. It then follows that withholding information should be more prevalent as a form of deception than active falsification of information because of the relative difficulties associated with detecting cheaters. Empirical studies of deception have focused on the benefits of cheating but have provided no data on the costs associated with being detected as a cheater. [Hauser] present[s] results from field experiments on rhesus monkeys (Macaca mulatta) which show that individuals discovering food announce their discoveries by calling on 45% of all trials. Discoverers who failed to call, but were detected with food by other group members, received significantly more aggression than vocal discoverers. Moreover, silent female discoverers ate significantly less food than vocal females. This demonstrates that there are significant costs to withholding information. Such costs may constrain the frequency with which deception occurs in this and other populations. Payoffs/Biological applications/Sociology and anthropology/Biological applications - specific species - rhesus monkeys.
• 75. Hemelrijk, C.K. 1991. "Interchange of 'Altruistic' Acts as an Epiphenomenon." Journal of Theoretical Biology 153:131-139.
  • Corrects error in 1990 article published in the same journal.- LD Draws a distinction between reciprocity (one kind of act exchanged for an act of the same kind) and interchange (barter of different kinds of acts). Studies reciprocity and interchange "among all pairs of groupmembers (i.e. at group level) as a correlation between an actor and a receiver matrix" (p. 137). Hemelrijk re-analyzed Seyfarth's (1980) data on wild female vervets. As a supplement to the correlation between grooming and received support discussed in her 1990 paper, she found that the reverse correlation between support and being groomed was also significant. However, the latter correlation could be explained as a side-effect of: 1) reciprocity in grooming and a relationship between the frequency of grooming and support; and 2) reciprocity of support and a correlation between received grooming and received support. This result is at odds with the interchange of support for being groomed suggested by Seyfarth and Cheney (1984). Interactions/Population structure/Biological applications/Biological applications - specific species - vervets.
• 76. Hemelrijk, C.K. 1990. "A Matrix Partial Correlation Test Used in Investigations of Reciprocity and Other Social Interaction Patterns at Group Level." Journal of Theoretical Biology 143:405-420.
  • Reciprocity and other social interaction patterns can be studied at two levels, within pairs (i.e. at dyadic level) and among pairs (i.e. at group level). In this paper advantages of the latter approach are emphasized. However, an analysis at group level implies the correlation of interaction matrices and because such data are statistically dependent, the significance of a correlation has to be calculated in a special way. This is done by means of Mantel's permutation procedure. In order to reckon with individual variation, Mantel's permutation procedure is used in combination with the so-called Kr statistic, whereby correlations are calculated simultaneously for each separate row. With the aid of the Kr test, the correlation for interchange of grooming for the receipt of "support" in conflicts in baboons and vervet monkeys [data from Seyfarth (1976, Anim. Behav. 24, 917-938, 1980, Anim. Behav. 28, 798-813)] was reconfirmed. However, this result may have arisen as a by-product of correlations with other variables. Therefore, the partial form of the Kr test is derived and applied to Seyfarth's data and it appears that the interchange of grooming for the receipt of "support" in conflicts, is indeed a spurious correlation in vervets but not in baboons. Direct tuning of grooming to the amount of received "support" thus seems therefore unlikely in case of the vervets, but may exist in the baboons. Some further suggestions are given about the way in which reciprocity/interchange may emerge as a by-product of simple (behavioural) rules. In certain behaviours (like for instance "reconciliation") missing values occur "conditionally", i.e. when the preceding behaviour (a fight in case of "reconciliation") was absent. The same Kr partial correlation test can be used in order to make efficient use of the existing data. This is illustrated with an example of a test for reciprocity of "tolerance" during food sharing among captive female chimpanzees. Interactions/Biological applications/Biological applications - specific species - chimpanzees.
• 77. Hemelrijk, Charlotte K. 1990. "Models of, and Tests for, Reciprocity, Unidirectionality and Other Social Interaction Patterns at a Group Level." Animal Behaviour 39:1013-1029.
  • Research on reciprocity is impaired by confusing definitions and often wrongly used statistical tests. Here, two models of the mechanism on which reciprocity is based are discussed and an initial step towards a new framework for its analysis is presented. A distinction is made between reciprocity and interchange. In the case of reciprocity, for one kind of act the same kind is received in return. In interchange, however, two different kinds of acts are bartered. Three types of reciprocity/interchange in social actions among all pairs of group-members are distinguished ('qualitative', 'relative' and 'absolute') on the basis of the precision of the reciprocity/interchange. Permutation procedures for association between matrices (such as the Mantel Z and two other newly derived tests) are used as a statistical test for detecting reciprocity/interchange. A rough comparison of the power of the two new tests is included. The tests can be applied to all kinds of group-living animals and to all sorts of social behaviour. The distinction between the three types of reciprocity/interchange and the matching statistical methods are also useful for defining and detecting other patterns in social interactions, like unidirectionality and associations between different kinds of social behaviour. The influence on social interactions of variables like dominance rank, age and sex can be analysed in the three forms by testing correlations between invented matrices which represent the influence of these variables (the so-called hypothesis matrices) and social interaction matrices. These methods are extended for two categories of individuals, thus allowing the investigation of, for example, reciprocity between males and females. The methods are illustrated with examples of coalition formation and grooming behaviour among captive chimpanzees, Pan troglodytes. Interactions/Biological applications/Biological applications - specific species - chimpanzees.
• 78. Hill, Greg. 1993, January. "From Stagnation to Recovery: A Prisoner's Dilemma and Its Solution." Challenge 36:61-62.
  • Looks at the question of cyclical periods of economic stagnation. Hill suggests that the investment decisions of firms in such a situation resemble a PD: firms are less willing to risk investment individually, although each firm would probably benefit from increased sales if other firms invested. Since it is in each firm's interest not to invest in the short run, no firms invest and the economy remains stagnant, so how does economic recovery ever begin? The neoclassical answer to this question is that interest rates fall in the stagnant period and individual firms then find it worthwhile to invest. The Keynesian answer to this question is that government invests first and thereby reduces the risk individual firms face. Hill notes that these solutions do not always work, and suggests a third possibility: government should reduce the length of economic stagnation by negotiating a solution or contract among firms in which all agree to invest simultaneously. - abstract by LD Economics and business.
• 79. Hirshleifer, David and Eric Rasmusen. 1989. "Cooperation in a Repeated Prisoners' Dilemma with Ostracism." Journal of Economic Behavior and Organization 12:87-106.
  • The unique Nash equilibrium of the finitely repeated n-person Prisoners' Dilemma calls for defection in all rounds. One way to enforce cooperation in groups is ostracism: players who defect are expelled. If the group's members prefer not to diminish its size, ostracism hurts the legitimate members of the group as well as the outcast, putting the credibility of the threat in doubt. Nonetheless, [the authors] show that ostracism can be effective in promoting cooperation with either finite or infinite rounds of play. The model can be applied to games other than the Prisoners' Dilemma, and ostracism can enforce inefficient as well as efficient outcomes. Interactions/Payoffs/Payoffs - comparing different PD matrices/Endogenous ending - ostracism/Population size/Population structure - information requirements/Norms/Economics and business/Sociology and anthropology/Deductive/Theory.
• 80. Hirshleifer, Jack and Juan Carlos Martinez Coll. 1992. "Selection, Mutation and the Preservation of Diversity in Evolutionary Games." Revista Espanola de Economia 9:251-273.
  • Evolutionary models suggesting that in mixed-motive situations only a single strategy, or only a single type of behavior, will ultimately prevail cannot be regarded as satisfactory. Among the forces supporting diversity of strategies and of behaviours are: (i) multiple and/or mixed evolutionary equilibria, (ii) mutation pressure, and (iii) transient dynamic processes. This paper studies the interaction of the archetype strategies COOPERATE versus DEFECT in Prisoners' Dilemma, and COWARD versus DAREDEVIL in Chicken, with two alternative reactive strategies TIT FOR TAT and BULLY. Only in exceptional limiting cases does a single strategy or a single form of behavior come to extinguish all others. TIT FOR TAT tends to support the predominance of nice behaviors in Prisoners' Dilemma (but not Chicken), while BULLY tends to support a predominance of mean behaviors generally. Payoffs/Payoffs - comparing different PD matrices/Population dynamics/Limited set of allowable rules - enumerated set/Theory/Simulation.
• 81. Huberman, Bernardo A. and Natalie S. Glance. 1993. "Evolutionary Games and Computer Simulations." Proceedings of the National Academy of Sciences, USA 90:7716-7718.
  • Huberman and Glance found greater cooperation between players with greater delays in updating information. - LD For other work on asynchronous choices, see H.A. Ceccatto and B.A. Huberman (1989) "Persistence of Nonoptimal Strategies." PNAS, USA 86:3443-3446. The Prisoner's Dilemma has long been considered the paradigm for studying the emergence of cooperation among selfish individuals. Because of its importance, it has been studied through computer experiments as well as in the laboratory and by analytical means. However, there are important differences between the way a system composed of many interacting elements is simulated by a digital machine and the manner in which it behaves when studied in real experiments. In some instances, these disparities can be marked enough so as to cast doubt on the implications of cellular automata-type simulations for the study of cooperation in social systems. In particular, if such a simulation imposes space-time granularity, then its ability to describe the real world may be compromised. Indeed, [Huberman and Glance] show that the results of digital simulations regarding territoriality and cooperation differ greatly when time is discrete as opposed to continuous. Population dynamics/Population structure - spatial models/Limited set of allowable rules - finite state machines/Automata theory/Simulation.
• 82. Hughes, Kirsty and Christine Oughton. 1993. "Diversification, Multi-market Contact and Profitability." Economica 60:203-224.
  • This paper analyses the relationships between diversification, multi-market contact and industry profitability. It focuses on the link between diversification and multi-market contact to show that, when diversification establishes or increases the extent to which firms meet in more than one market, the effect of such multi-market contact is to increase the possibility that collusion emerges as an evolutionarily stable strategy. As a result, multi-market contact may increase the potential for tacit collusion and so lead to higher profitability. The effects of diversification and multi-market contact on the price-cost margin and the rate of return to capital are estimated using a specially constructed new database for UK manufacturing industry in 1979. This database provides information on the diversification and multi-market contact of 418 firms across 134 manufacturing industries, thus linking firm- and industry-level data. The results show a clear positive effect of multi-market contact on industry profitability. Economics and business/Deductive/Empirical.
• 83. Ickes, Barry W. and Larry Samuelson. 1987. "Job Transfers and Incentives in Complex Organizations: Thwarting the Ratchet Effect." RAND Journal of Economics 18:275-286.
  • Many complex organizations, such as planned Soviet enterprises and the U.S. military, routinely transfer employees between jobs. Since this sacrifices job-specific human capital, the practice is puzzling. This article shows that regular job transfers may be part of an optimal incentive scheme in organizations plagued by the ratchet effect. The ratchet effect arises when an employer is uncertain as to the productivity of the various positions or jobs within an organization. Workers in highly productive jobs then have an incentive to disguise the productivity of their jobs by expending low effort and producing low output. This avoids having the employer construct more demanding renumeration schemes once the high productivity of a job becomes known. Job transfers break the link between current performance and future incentive schemes, and hence remove the incentive-stifling implications of the ratchet effect. This article examines the tradeoff between providing more effective incentives via job transfers and the accompanying sacrifice of job-specific human capital, establishes conditions under which job transfers are optimal, and develops comparative static results. Payoffs/Limited set of allowable rules - limited rationality/Economics and business/Deductive/Collateral research.
• 84. Ikegami, Takashi and Kunihiko Kaneko. 1990. "Computer Symbiosis - Emergence of Symbiotic Behavior through Evolution." Physica D 42:235-243.
  • Symbiosis is cooperation between distinct species. It is one of the most effective evolutionary processes, but its dynamics are not well understood as yet. A simple model of symbiosis is introduced, in which [the authors] consider interactions between hosts and parasites and also mutations of hosts and parasites. The interactions and mutations form a dynamical system on the populations of hosts and parasites. It is found that a symbiotic state is not static, but dynamically oscillates. Harmful parasites violating symbiosis appear periodically, but are rapidly extinguished by hosts and other parasites, and the symbiotic state is recovered. The relation between these phenomena and "TIT for TAT" strategy to maintain symbiosis is discussed. Population dynamics/Biological applications/Theory/Simulation.
• 85. Insko, Chester A., John Schopler, Stephen M. Drigotas, Kenneth A. Graetz, James Kennedy, Chante Cox and Garry Bornstein. 1993. "The Role of Communication in Interindividual-Intergroup Discontinuity." Journal of Conflict Resolution 37:108-138.
  • The present research was designed to explore the role of communication on interindividual-intergroup discontinuity in the context of the PDG-Alt matrix. (The PDG-Alt matrix is a prisoner's dilemma game matrix that adds a third withdrawal choice to the usual cooperative and uncooperative choices of the PDG matrix, and interindividual-intergroup discontinuity is the tendency of intergroup relations to be more competitive and less cooperative than interindividual relations.) Several predictions implied by the fear and greed explanations of interindividual-intergroup discontinuity were tested. One prediction, an implication of the fear hypothesis, is that communication should produce a larger increase in the cooperation of individuals than of groups. This prediction is based partially on the assumption that the outgroup schema, which leads to more fear of groups than of individuals, should reduce the credibility of between group communication. Given, however, that without communication individuals may not cooperate, what will they do? Will they withdraw or will they compete? Another prediction, an implication of the greed hypothesis, is that the absence of communication should result in a greater increase in withdrawal for individuals than for groups. This prediction is based partially on the assumption that the social support provided to fellow group members for self-interested competitiveness is absent for individuals. These predictions were confirmed. It was argued that the lesser tendency of individuals to cooperate when there is no communication with the opponent may explain partially the differing results of past discontinuity research (which has involved communication) and research reported in the PDG literature (which typically has not involved communication). Choices/Endogenous ending - voluntary exit/Population size/Sociology and anthropology/Psychology.
• 86. Irons, William. 1991. "How Did Morality Evolve?" Zygon 26:49-89.
  • This paper presents and criticizes Alexander's evolutionary theory of morality (1987). Earlier research, on which Alexander's theory is based, is also reviewed. The propensity to create moral systems evolved because it allowed ancestral humans to limit conflict within cooperating groups and thus form larger groups, which were advantageous because of intense between-group competition. Alexander sees moral codes as contractual, and the primary criticism of his theory is that moral codes are not completely contractual but also coercive. Ways of evaluating Alexander's theory as well as modified versions of it are discussed. Norms/Reputation/Sociology and anthropology.
• 87. Jablonowski, Mark. 1986. "Does Workable Competition Exist in the Property/Casualty Industry?" CPCU Journal 39:248-251.
  • Perfectly competitive markets yield social welfare benefits, but perfect markets are rare among modern American industries. However, social welfare benefits can exist when markets are workably competitive. Workable competition yields social benefits, but in such markets there is no clear means through which public policy actions would result in social benefit gains rather than losses. Jablonowski considers the case of the property and casualty insurance industry, important because of its size and the potential for costly disasters. Earnings in the insurance industry follow a pattern known as the underwriting cycle. The logic of this cycle parallels that of the PD. High earnings represent cooperative behavior among firms charging high prices. Declines in earnings are associated with price wars or defections of firms from charging a higher price. The earnings cycle suggests that a severe price instability exists in the market, independent of changes in market demand or costs of production. Jablonowski concludes that public policy action to correct for the price instability and to realize higher social benefits is problematic. It is not clear what incentives would be needed to induce firms to sacrifice potentially high but short term earnings. - abstract by LD Economics and business.
• 88. Jablonowski, Mark. 1988. "A Game-Theoretic Analysis of Insurer Behavior." CPCU Journal 41:117-121.
  • Game theory is an effective tool for analyzing the behavior of interdependent firms because it recognizes that one firm's outcome depends on the choices other players make. The property and casualty insurance industry might be described as a loose oligopoly, so one might expect some interdependence to have developed among firms. Jablonowski suggests that the PD may represent that fundamental characteristics of an oligopoly; if oligopolies want to achieve cooperation in repeated play, they need to police against the defections of other players. He briefly discusses extending the game to n players and methods of analyzing complex games. He concludes by noting that few detailed game theoretic analyses of industries exist, in part because business people will not discuss market strategies openly. - abstract by LD Interactions/Economics and business.
• 89. Jablonowski, Mark. 1987, July. "Insurance and Game Theory." Best's Review: Property/Casualty Insurance Edition 88:38-40.
  • Argues that game theory may be more useful than Adam Smith's theory of the invisible hand for understanding the behavior of interdependent firms. He uses a PD to illustrate a simple market where two firms have the choice to price high (cooperate) or low (defect). He argues that repeated play does not solve the dilemma, since the possibility of double crossing the other player always exists. He uses the PD example to provide a possible explanation for the underwriting cycle in the insurance industry. Firms want to cooperate and charge the high price, but some firms will defect. Eventually the non-defectors discover this, and they reduce their prices and maintain these lower rates for a while in order to encourage defectors to return to a higher pricing strategy. While the PD provides a plausible explanation, Jablonowski argues that the industry does not know enough about insurance companies' choices and goals to exploit game theory fully. - abstract by LD Economics and business.
• 90. James, Patrick and Frank Harvey. 1992. "The Most Dangerous Game: Superpower Rivalry in International Crises, 1948-1985." Journal of Politics 54:25-53.
  • Crises involving the superpowers as adversaries pose a serious threat to the survival of the global system. The present investigation will focus on patterns of response when one superpower is faced with a crisis resulting from a threat attributed to the other. The objective is to determine which among several strategic options characterizes superpower reactions. With that priority in mind, there will be four stages to the inquiry. First, several models for transforming conflict into cooperation will be presented in abstract terms. The second task is to operationalize these models with an emphasis on identifying strategic options that might be pursued in superpower crises. Third, data from the International Crisis Behavior Project will be used to test the predictive power and general relevance of the strategic options derived from the models. Fourth, and finally, the significance of the results and directions for further research will be discussed. Payoffs/Payoffs - comparing different PD matrices/Limited set of allowable rules - enumerated set/Limited set of allowable rules - limited rationality/Politics and law - international/Deductive/Empirical.
• 91. Joshi, N.V. 1987. "Evolution of Cooperation by Reciprocation within Structured Demes." Journal of Genetics 66:69-84.
  • The iterative two-person Prisoners' Dilemma game has been generalised to the N-person case. The evolution of cooperation is explored by matching the Tit For Tat (TFT) strategy (Axelrod and Hamilton 1981) against the selfish strategy. Extension of TFT to N-person situations yields a graded set of strategies from the softest TFT, which continues cooperation even if only one of the opponents reciprocates it, to the hardest, which would do so only when all the remaining opponents cooperate. The hardest TFT can go to fixation against the selfish strategy provided it crosses a threshold frequency pc. All the other TFT are invadable by the selfish (D) or the pure defector strategy, while none can invade D. Yet, provided a threshold pc is crossed, they can coexist stably with D. As N, the size of the group increases, the threshold pc also increases, indicating that the evolution of cooperation is more difficult for larger groups. Under certain conditions, only the soft TFT can coexist stably against the selfish strategy D, while the harder ones cannot. An interesting possibility of a complete takeover of the selfish population by successive invasions by harder and harder TFT strategies is also presented. Interactions/Payoffs - comparing different PD matrices/Population dynamics - ESS/Population dynamics - replicator dynamics/Population size/Limited set of allowable rules - enumerated set/Theory/Deductive.
• 92. Kahn, Lawrence M. and J. Keith Murnighan. 1993. "Conjecture, Uncertainty, and Cooperation in Prisoner's Dilemma Games." Journal of Economic Behavior and Organization 22:91-117.
  • This paper presents experimental tests of two models of cooperation in finitely-repeated prisoner's dilemma games (Kreps, Milgrom, Roberts, and Wilson, 1982). The models suggest that either a perception that the other party may use the tit-for-tat strategy or mutual uncertainty concerning dominant noncooperative strategies can lead to rational cooperation. The experiment independently manipulated both types of uncertainty and allowed for inferences concerning the players' prior, 'homemade' preferences for cooperation. Only in relatively restricted situations did either type of uncertainty promote cooperation. Instead, players cooperated much more than was predicted; they also cooperated more when they were certain of their opponents' payoffs. Payoffs - comparing different PD matrices/Limited set of allowable rules - limited rationality/Psychology/Empirical.
• 93. Kalai, Ehud and William Stanford. 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games." Econometrica 56:397-410.
  • A measure of complexity for repeated game strategies is studied. This measure facilitates the investigation of some issues regarding finite rationality and the structure of subgame perfect equilibria of repeated games with discounting. Specifically, the complexity of a strategy in a given repeated game is defined to be the cardinality of the induced strategy set, i.e., the number of distinct strategies induced by the original strategy in all possible subgames. [The authors] observe that this cardinality is equal to the size (cardinality of the state set) of the smallest automaton which can implement the strategy. Thus, in a sense, complexity is measured on the basis of the amount of computing power inherent in the strategy. A measure of strategic memory is also studied. The following results are obtained: (1) combining two notions of bounded rationality (epsilon equilibrium and finite complexity), [the authors] find that every subgame perfect equilibrium of the repeated game can be approximated (with regard to payoffs) by a subgame perfect epsilon equilibrium of finite complexity. (2) For