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I present a game-theoretic model of an Epicurean State of Nature based upon Epicurus’ proto-evolutionary account of human development. I argue that for Epicurus the State of Nature has at least two stages. I model the first stage, where according to Epicurus the adult humans lead mainly solitary lives and are all roughly equally capable of harming each other, as an extension of the Hawk-Dove game where agents can follow a contingency strategy. I argue that at this first stage the individuals are likely to converge to a contingency strategy convention where they generally avoid conflict. I model the second stage, where according to Epicurus families emerge and join to form communities, by introducing heterogeneity with respect to ability to harm into the population engaging in the extended Hawk-Dove game of the first stage. In particular, in some extended Hawk-Dove encounters weakagents who are relatively vulnerable members of some families encounter strongcounterpart agents who belong to other families. I argue that this heterogeneity can result in the population converging to an equilibrium corresponding to a State of Nature war. I conclude Epicurus can reach a conclusion similar to Hobbes’ conclusion that war is inevitable in a State of Nature. But Epicurus would arrive at this Hobbesian conclusion by a rather un-Hobbesian route, for the supporting argument relies upon significant inequalitiesin powers among the residents of the State of Nature.

I propose a dynamical analysis of interaction in anarchy, and argue that this kind of dynamical analysis is a more promising route to predicting the outcome of anarchy than the more traditional a priorianalyses of anarchy in the literature. I criticize previous a priorianalyses of anarchy on the grounds that these analyses assume that the individuals in anarchy share a unique set of preferences over the possible outcomes of war, peace, exploiting others and suffering exploitation. Following Hobbes classic analysis of anarchy, I maintain that typically in anarchy some moderateindividuals will most desire mutual cooperation while other dominatorswill most desire to exploit others cooperation. I argue that once one allows for different types of individuals in anarchy, any a priorianalysis of anarchy requires unrealistic assumptions regarding the agents common knowledge of their situation. However, this move also suggests a dynamical analysis of anarchy, one that assumes no common knowledge. In the Variable Anticipation thresholdmodel developed here, individuals modify their behavior as they learn from repeated interactions. I present specific instances of this model where the individuals in anarchy converge to different equilibria corresponding to either peace or war, depending on the initial conditions. I show that individuals are liable to converge to Hobbes war of all against all even if only a small percentage of are dominators. The presence of only a few “nasty” individuals gradually drives all, including those inclined to be “nicer”, to imitate the “nasty” conduct of these few. This dynamic analysis suggests that the Hobbesian war in anarchy is indeed inevitable in most realistic circumstances.You have the same propension, that I have, in favor of what is contiguous above what is remote. You are, therefore, naturally carryd to commit acts of injustice as well as I. Your example both pushes me forward in this way by imitation, and also affords me a new reason for any breach of equity, by showing me, that I shoud be the cully of my integrity, if I alone shoud impose on myself a severe restraint amidst the licentiousness of others. (David Hume, A Treatise of Human Nature)

Learning to take turns in repeated game situations is a robust phenomenon in both laboratory experiments and in everyday life. Nevertheless, it has received little attention in recent studies of learning dynamics in games. We investigate the simplest and most obvious extension of fictitious play to a learning rule that can recognize patterns, and show how players using this rule can spontaneously learn to take turns.

Abstract:In recent years, a number of authors have used game-theoretic reasoning to explain why purely self-interested agents would ever conform their economic activities with the requirements of justice, when by doing so they forego opportunities to reap unilateral net gains by exploiting others. In this paper, I argue that Hume’s justification of honest economic exchanges between self-interested agents in the Treatiseforeshadows this contemporary literature. Hume analyzes the problem of explaining justice in self-interested economic exchange as a problem of agents coordinating on a pattern of reciprocal cooperation, as opposed to some other behavioral pattern such as reciprocal exploitation, in exchanges repeated over time. Hume’s arguments anticipate informally the contemporary interpretation of just economic practices as forming part of an equilibrium of a repeated game. I close the paper by arguing that Hume does not provide a satisfactory explanation of how the mutual expectations that support justice in economic exchange arise in a community of self-interested agents. The problem Hume leaves unsolved is one of equilibrium selection, that is: Why do agents follow an equilibrium corresponding to just economic exchanges rather than some other equilibrium corresponding to unjust exchanges? I also argue that contemporary game theory still lacks a satisfactory theory of equilibrium selection, but that such a theory would lead us closer to a satisfactory Humean reconciliation of justice and self-interest in economic exchange.

In 1954, Richard Braithwaite chose as the topic of his inaugural lecture at Cambridge The Theory of Games as a Tool for the Moral Philosopher. Braithwaite argued that by using the recently developed mathematical theory of games, philosophers could resolve certain problems in moral philosophy previously considered unsolvable. Formal game theory is a product of the twentieth century. John von Neumann and Oskar Morgenstern established game theory as an important new branch of social science with the publication of their 1944 treatise Theory of Games and Economic Behavior. However, the basic idea that motivates game theory has much older intellectual roots in the work of philosophers such as Hobbes (1651) and Hume (1740). This basic idea can be expressed in the following way: How agents behave in a given social interaction depends crucially upon their reciprocal expectations. To give an example adapted from Braithwaite’s lecture, if you and I wish to have a telephone conversation, then exactly one of us must call. I should wait for your call precisely when I expect you to call, which you should do when you expect me to wait. Even in an example this simple, issues of fairness can come into play. We both want to coordinate our behavior and have our telephone chat. But each of us mayprefer tocall, so as to avoid having the other pay for the call. Braithwaite used game theory to model this example, and to propose a method for assigning the roles of caller and receiver equitably. He conjectured that this method could be applied in general to problems of distributive justice.

Aconvention is a state in which agents coordinate their activity, not as the result of an explicit agreement, but because their expectations are aligned so that each individual believes that all will act so as to achieve coordination for mutual benefit. Since agents are said to follow a convention if they coordinate without explicit agreement, the notion raises fundamental questions: (1) Why do certain conventions remain stable over time?, and (2) How does a convention emerge in the first place? In a pioneering study, Lewis (1969) addresses these questions by applyingnoncooperative game theory. Lewis defines a convention as aNash coordination equilibrium of a noncooperative game that issalient, that is, it is somehow conspicuous to the agents so that all expect one another to conform with the equilibrium. This paper presents a new game theoretic definition of conventions, which formalizes the notion of salience and which also generalizes the class of conventions Lewis discusses in his work. I define a convention as acorrelated equilibrium (Aumann 1974, 1987) satisfying apublic intentions criterion: Every agent wants his intended action to becommon knowledge. I argue that many conventions correspond to correlated equilibria that are not Nash equilibria, and that this is consistent with Lewis' general viewpoint. Finally, I argue that game theoretic characterizations of convention, such as Lewis' and my own, help to explain a convention's stability, but that a fully satisfactory account of the emergence of convention requires a theory of equilibrium selection beyond the scope of Lewis' work.