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This chapter presents and proves the folk theorem for games of perfect monitoring. The chapter first proves the folk theorem for two players with public correlation and pure-action individual rationality. This is then generalized to arbitrary numbers of players, via both a dimensionality assumption on feasible payoffs and the idea of non-equivalent utilities, then to games without public correlation and finally to mixed-action individually rational payoffs.

This chapter shows that in many situations with patient players, the payoffs bounds from Chapter 8 are tight. It then proves various folk theorems for games of public monitoring, including games with a product structure and extensive form games. The chapter discusses the enforceability, identifiability, and rank conditions on the monitoring technology required for the folk theorem, and finally considers games of symmetric incomplete information.

The folk theorem shows that cooperative behavior can be sustained as a Nash equilibrium in indefinitely repeated games — a phenomenon known as reciprocal altruism. The same theorem offers a solution to various other social mysteries. Who guards the guardians? How are authority, blame, courtesy, dignity, envy, friendship, guilt, honor, integrity, justice, loyalty, modesty, ownership, pride, reputation, status, trust, virtue, and the like to be explained as emergent phenomena? How do beliefs that many people privately know to be false survive?

This chapter explores variations on the standard repeated game: random matching games and repeated games played in the context of a market or society, multiple repeated games, repeated extensive form games, and dynamic games. The chapter defines and provides foundations for the concept of Markov equilibrium and culminates in a folk theorem for dynamic games.

This chapter studies games played by the same players over and over again. The strategies in repeated games are modeled as finite automata, and a version of the folk theorem is proved. This says that full cooperation can be sustained as an equilibrium outcome in a repeated situation under suitable conditions. The folk theorem is perhaps the most important result that game theory has to offer to social philosophy. Its relevance to social contract theory is briefly explored by showing how it can explain such emergent phenomena as trust, authority, and altruism. The chapter ends by drawing attention to the fact that Axelrod's claims for the strategy tit-for-tat are seriously misleading.

This chapter provides a detailed treatment of work on games with almost-public monitoring. The chapter introduces the key distinction between strategies with bounded and unbounded recall, showing that perfect public equilibria with bounded recall in public monitoring games induce equilibrium behavior in nearby private monitoring games, while equilibria with unbounded recall typically imply coordination failure in nearby private monitoring games. The chapter concludes with a folk theorem for games of almost-public monitoring.

The folk theorem requires that each action taken by each player carry a signal that is conveyed to the other players. A signal is imperfect if all players receive the same signal; the signal is perfect if it accurately reports the player's action. The question of the signal quality required to obtain efficient cooperation is especially critical when the size of the game is considered. Generally, the folk theorem does not even mention the number of players, but in most situations in real life, the larger the number of players participating in a cooperative endeavor, the lower the average quality of the cooperation vs. defection signal because generally a player observes only a small number of other players with a high degree of accuracy, however large the group involved. This chapter explores this issue and illustrates the problem by applying the Fudenberg et al. (1994) framework to the Public Goods Game, which in many respects is representative of contexts for cooperation in humans.

This chapter examines whether recent advances in the theory of repeated games, as exemplified by the so-called folk theorem and related models, address the shortcomings of the self-interest based models in explaining human cooperation. It first provides an overview of folk theorems and their account of evolutionary dynamics before discussing the folk theorem with either imperfect public information or private information. It then considers evolutionarily irrelevant equilibrium as well as the link between social norms and the notion of correlated equilibrium. While the insight that repeated interactions provide opportunities for cooperative individuals to discipline defectors is correct, the chapter argues that none of the game-theoretic models mentioned above is successful. Except under implausible conditions, the cooperative outcomes identified by these models are neither accessible nor persistent, and are thus labeled evolutionarily irrelevant Nash equilibria.

This lecture gives a brief overview of an evolutionary theory of fairness. Most of the ideas discussed in the lecture can be found in the book Natural Justice. The lecture begins by determining how and why the norms of fairness evolved, and examines the device of the original position. This device is the stylised form of the common structure underlying all fairness norms. The lecture then looks at the possibility of having justice as fairness, pure foraging societies, and the basics of game theory. Coordination games, reciprocity, the folk theorem, selecting equilibria, and the deep structure of fairness are some of the concepts discussed in detail in this lecture.

Repeated games are considered. The discussion explains issues surrounding randomization, observability, feasibility, and convexity. Games with pay-off averaging and discounting are examined, along with finitely repeated games. The ‘no-gain-from-one-shot-deviation’ property of games with continuous pay-offs is discussed and the proof sketched. Finally, games of incomplete information are introduced.

The Reconciliation Project, the attempt to show that justice is compatible with rational prudence, is evaluated in light of the classic challenges of Hobbes’ Foole, Plato’s Lydian Shepherd, and Hume’s Sensible Knave. Hobbes’ response to the Foole is justice-reciprocalist, emphasizing social sanctions, and is naturally interpreted in terms of folk theorem interactions of repeated games. Plato’s justice-Platonist response to the Shepherd, who has identity-concealing power, emphasizes goods allegedly inseparable from justice. A new Invisible Foole challenge is considered where an agent like the Foole who takes seriously only social sanctions acquires identity-concealment technology, and folk theorem responses are proposed for this challenge. The Invisible Foole challenge is similar to the most serious challenge, that of the Sensible Knave. The most compelling response to the Knave’s challenge combines elements of justice-reciprocalism and justice-Platonism.

This chapter discusses the games played in real life with emphasis on how these are played. It examines reciprocity as the glue that holds human societies together, as the key to human cooperation, and an important element in repeated games. Repeated games give rise to the folk theorem where all Nash equilibrium outcomes consist of all points in the cooperative payoffs where all the players feel secure. This case shows why players usually steadfastly stick to their strategies, or punish a deviant opponent. This chain of responsibility explains why social contracts form the basic principle of some aspects of society. This theorem also explains why concepts like reputation and trust matter so much in human societies.

This chapter opens with a simple diagram capturing the tension that all social creatures face between self interest and the social good. It then reviews two famous devices for alleviating the tension, Hamilton’s kin selection and Trivers’s bilateral reciprocity, and demonstrates their isomorphism. Next it reviews the “kaleidoscope” niches that our ancestors inhabited in Pleistocene times, emphasizing the intense selection for flexible forms of cooperation within stable groups of individuals. It then presents humans’ novel coping device, the moral system, which builds on but goes well beyond the earlier devices. It shows how the content of the moral code evolves on short timescales to adapt to novel environments, and concludes with a short discussion of new adaptations (e.g., egalitarian to hierarchical) to accommodate pastoral life styles 10 thousand years ago.

This chapter defends an essentially individualist model of the evolution of cooperation amongst Pleistocene foragers. The chapter argues that these foragers satisfied the conditions of the “folk theorem” of stable reciprocation-based cooperation. Their social groups were small and stable, with very high probabilities of future interaction. They were informationally transparent: reputation was very reliable. The rewards of cooperation were high, and the temptations to defect were rarely large. The costs of sanctioning defection were typically modest, and reputation was reliable enough and valuable enough to make investments in reputation through cooperating in controlling defection worth paying. Foragers cooperated because it was almost always in their individual interest to do so. The chapter argues against the idea that group selection drove the evolution of foraging cooperation; these views underestimate the costs of conflict; overestimate its benefits, and are not supported by the archaeological record. Third, the chapter shows that the selective environment changed at the Pleistocene-Holocene transition, as groups became sedentary and larger. These changes eroded the forager equilibrium, moreover group-group conflict is much more significant in the archaeological record from this time. While much remains unclear about the origins of farming and more complex social units, it is clear that the evolutionary basis of cooperation changed radically through this transition.

For a given division of labor, (potential) breakdowns of integration can be traced to either motivational or knowledge-related sources (or both). Integration failures arising from coordination problems require managing the need for and/or the extent of predictive knowledge; those arising from cooperation problems require managing the valence of interdependence. A fruitful area for further enquiry awaits the student of organization design at the intersection of these sources of integration failure. I outlined two possible approaches: a closer look at the interactions between knowledge and motivation-related issues, or a coarser bundling of both into the construct of integration. In particular, given the behavioral assumptions of adaptive rationality, thinking of integration of effort as a search problem may be an area of high research potential. It can help understand organizations as “marvels but not miracles”—how boundedly rational designers can nevertheless organize boundedly rational agents towards accomplishing goals.