The Pasadena game is an example of a decision problem which lacks an expected value, as traditionally conceived. Easwaran (2008) has shown that, if we distinguish between two different kinds of expectations, which he calls ‘strong’ and ‘weak’, the Pasadena game lacks a strong expectation but has a weak expectation. Furthermore, he argues that we should use the weak expectation as providing a measure of the value of an individual play of the Pasadena game. By considering a modified version of (...) the Pasadena game, I argue that weak expectations may provide a very poor measure of the value of an individual play of the game, and hence should not be used to value individual plays unless further information is taken into consideration. (shrink)

The advent of functional brain imaging has revolutionized the ability to understand the biological mechanisms underlying decision-making. Although it has been amply demonstrated that assumptions of rationality often break down in experimental games, there has not been an overarching theory of why this happens. I describe recent advances in functional brain imaging and suggest a framework for considering the function of the human reward system as a discrete agent.

The difficulty of defining rational behavior in game situations is that the players'' strategies will depend on their expectations about other players'' strategies. These expectations are beliefs the players come to the game with. Game theorists assume these beliefs to be rational in the very special sense of beingobjectively correct but no explanation is offered of the mechanism generating this property of the belief system. In many interesting cases, however, such a rationality requirement is not enough to guarantee that an (...) equilibrium will be attained. In particular, I analyze the case of multiple equilibria, since in this case there exists a whole set of rational beliefs, so that no player can ever be certain that the others believe he has certain beliefs. In this case it becomes necessary to explicitly model the process of belief formation. This model attributes to the players a theory of counterfactuals which they use in restricting the set of possible equilibria. If it were possible to attribute to the players the same theory of counterfactuals, then the players'' beliefs would eventually converge. (shrink)

An information completion of an extensive game is obtained by extending the information partition of every player from the set of her decision nodes to the set of all nodes. The extended partition satisfies Memory of Past Knowledge (MPK) if at any node a player remembers what she knew at earlier nodes. It is shown that MPK can be satisfied in a game if and only if the game is von Neumann (vN) and satisfies memory at decision nodes (the restriction (...) of MPK to a player's own decision nodes). A game is vN if any two decision nodes that belong to the same information set of a player have the same number of predecessors. By providing an axiom for MPK we also obtain a syntactic characterization of the said class of vN games. (shrink)

The notion of perfect recall in extensive games was introduced by Kuhn (1953), who interpreted it as "equivalent to the assertion that each player is allowed by the rules of the game to remember everything he knew at previous moves and all of his choices at those moves''. We provide a characterization and axiomatization of perfect recall based on two notions of memory: (1) memory of past knowledge and (2) memory of past actions.

A generation of social theorists have argued that if free-rider considerations show that certain collective action predicaments are unresolvable under individual, rational choice – unresolvable under an arrangement where each is free to pursue their own relative advantage – then those considerations will equally show that the predicaments cannot be resolved by recourse to norms (Buchanan, 1975, p. 132; Heath, 1976, p. 30; Sober and Wilson, 1998, 156ff; Taylor, 1987, p. 144). If free-rider considerations explain why people do not spontaneously (...) keep the streets clean, though they would each prefer unlittered streets, then those considerations will also explain why there is no effective norm against littering the streets. (shrink)

The notion of a spontaneous social order, an order in human affairs which operates without the intervention of any directly ordering mind, has a natural fascination for social and political theorists. This paper provides a taxonomy under which there are two broadly contrasting sorts of spontaneous social order. One is the familiar invisible hand; the other is an arrangement that we describe as the intangible hand. The paper is designed to serve two main purposes. First, to provide a pure account (...) of the invisible hand, with some indication of the varieties of invisible hand (and, indeed, backhand) available. Second, to develop and motivate the unfamiliar conception of the intangible backhand. We believe that a recognition of the availability of this latter sort of spontaneous organising mechanism — and the mechanism is implicitly recognised in many traditions — is of great importance in political theory; it is of particular importance nowadays when the usual focus is entirely on the invisible hand. (shrink)

Although Colman's criticisms of orthodox game theory are convincing, his assessment of progress toward construction of an alternative is unnecessarily restrictive and pessimistic. He omits an important multidisciplinary literature grounded in human evolutionary biology, in particular the existence and function of social emotions experienced when facing some strategic choices. I end with an alternative suggestion for modifying orthodox game theory.

A syntactic formalism for the modeling of belief revision in perfect information games is presented that allows to define the rationality of a player's choice of moves relative to the beliefs he holds as his respective decision nodes have been reached. In this setting, true common belief in the structure of the game and rationality held before the start of the game does not imply that backward induction will be played. To derive backward induction, a “forward belief” condition is formulated (...) in terms of revised rather than initial beliefs. Alternative notions of rationality as well as the use of knowledge instead of belief are also studied within this framework. Footnotes1 I would like to thank Wlodek Rabinowicz and three anonymous referees for very helpful comments. (shrink)

In this paper, I develop a syntactic framework for the analysis ofstrategic form games that is based on a straightforward combination ofstandard systems of doxastic, probabilistic and conditionalpropositional logic. In particular, for the probabilistic part I makeuse of the axiomatization provided in Fagin and Halpern (1994). The use ofconditionals allows to represent a strategic form game by a logicalformula in a very natural way. Also expected utility maximization can benaturally captured. I use this framework to prove a version of a (...) resulton Nash equilibrium conjectures first presented in Aumann and Brandenburger (1995). (shrink)

Even if game theory is broadened to encompass other-regarding preferences, it cannot adequately model all aspects of interactive decision making. Payoff dominance is an example of a phenomenon that can be adequately modeled only by departing radically from standard assumptions of decision theory and game theory – either the unit of agency or the nature of rationality. (Published Online April 27 2007).

The paper argues that the Nash Equilibrium Refinement Programme in game theory was less successful than its competitor, the Epistemic Programme (Interactive Epistemology). The prime criterion of success is the extent to which the programmes were able to reach the key objective guiding non-cooperative game theory for much of the 20th century, namely, to develop a complete characterisation of the strategic rationality of economic agents in the form of the ultimate game theoretic solution concept for any normal form and extensive (...) game. The paper explains this in terms of unjustified degrees of mathematisation in the Nash Equilibrium Refinement Programme. While this programme's mathematical models were often inspired by purely mathematical concerns rather than the economic phenomena they were intended to be mathematical models of, the Epistemic Programme's mathematical models were developed with a keen eye to the role beliefs and desires play in strategic interaction between rational economic agents playing games; that is, their Interactive Epistemology. The Epistemic Programme succeeded in developing mathematical models formalising aspects of strategic interaction that remained implicit in the Nash Equilibrium Refinement Programme due to an unjustified degree of mathematisation. As a result, the Epistemic Programme is more successful in game theory . (shrink)

Using epistemic logic, we provide a non-probabilistic way to formalise payoff uncertainty, that is, statements such as ‘player i has approximate knowledge about the utility functions of player j.’ We show that on the basis of this formalisation common knowledge of payoff uncertainty and rationality (in the sense of excluding weakly dominated strategies, due to Dekel and Fudenberg (1990)) characterises a new solution concept we have called ‘mixed iterated strict weak dominance.’.

It is commonly believed that when a finite value is received in a game that has an infinite expected value, it is in one’s interest to redo the game (note that switching to an unknown but already determined value is equivalent to redoing). We have argued against this belief, at least in the repeated St Petersburg two-envelope case. We have also shown an example where repeatedly switching to a higher expected value leads to a worse outcome over any finite number (...) of trials. Finally, over infinitely many trials of the repeated St Petersburg two-envelope game, the always-switch strategy is paradoxically both better than and the same as the always-stay strategy. (shrink)

This volume presents mathematical game theory as an interface between logic and philosophy.

Colman proposes that the domain of interpersonal choice requires an alternative and nonindividualistic conception of rationality. However, the anomalies he catalogues can be accounted for with less radical departures from orthodox rational choice theory. In particular, we emphasize the need for descriptive and prescriptive rationality to incorporate recursive interplay between one's own choices and one's expectation regarding others' choices.

When a person performs a certain action, it signifies that he is causing a certain event to occur. Therefore the action is conveying a certain true sentence. Playing a game is a mutual activity, namely the listener and the speaker undertake an exchange through a linguistic dialogue or communicate through action. Because of the peculiar nature of the action, the actions in games belong to an activity where the speaker speaks true words and the listener hears true words. A static (...) game is a process through which the participants are simultaneously speaking and listening ; and a dynamic game is a process where speaking and listening take place in turn. Each step of a dynamic game is a speaking-listening exchange. Through listening and speaking, changes in the epistemic states of the participants occur. Of course, the degree of change depends on the type of game being played. In a dynamic game, each participant proceeds through a process of induction, and thus forms new epistemic states. (shrink)

The paper is a discussion of the interpretation of game theory. Game theory is viewed as an abstract inquiry into the concepts used in social reasoning when dealing with situations of conflict and not as an attempt to predict behavior. The first half of the paper..

In abductive planning, plans are constructed as reasons for an agent to act: plans are demonstrations in logical theory of action that a goal will result assuming that given actions occur successfully. This paper shows how to construct plans abductively for an agent that can sense the world to augment its partial information. We use a formalism that explicitly refers not only to time but also to the information on which the agent deliberates. Goals are reformulated to represent the successive (...) stages of deliberation and action the agent follows in carrying out a course of action, while constraints on assumed actions ensure that an agent at each step performs a specific action selected for its known effects. The result is a simple formalism that can directly inform extensions to implemented planners. (shrink)

We develop a multi-agent deontic action logic to study the logical behaviour of two types of deontic conditionals: (1) conditional obligations, having the form "If group H were to perform action aH, then, in group F's interest, group G ought to perform action aG" and (2) conditional permissions, having the form "If group H were to perform action aH, then, in group F's interest, group G may perform action aG". First, we define a formal language for multi-agent deontic action logic (...) and a class of consequentialist models to interpret the formulas of the language. Second, we define a transformation that converts any strategic game into a consequentialist model. Third, we show that an outcome a* is a Nash equilibrium of a strategic game if and only if a conjunction of certain conditional permissions is true in the consequentialist model that results from the transformation of that strategic game. (shrink)

This commentary focuses on the parts of psychological game theory dealing with preference, as illustrated by team reasoning, and supports the conclusion that these theoretical notions do not contribute above and beyond existing theory in understanding social interaction. In particular, psychology and games are already bridged by a comprehensive, formal, and inherently psychological theory, interdependence theory (Kelley & Thibaut 1978; Kelley et al. 2003), which has been demonstrated to account for a wide variety of social interaction phenomena.

Equilibrium game theory borrows from neoclassical economics its rationality concept which it immediately puts to work in order to produce the basic results it needs for building an elaborate narrative of social interaction. This paper focuses on some recent objections to game theory's use of rationality assumptions in general, and of backward induction and subgame perfection in particular, and interprets them in the light of the postmodern critique of the grand meta-narratives which social theorists often rely on for social explanation. (...) The paper presents a defence of game theory which seeks to accommodate the postmodern critique. However, it goes on to show that such a defence is illegitimate and claims that the problem lies with the faulty conceptualisation of the main concept on which game theory rests: that of Reason. Having established the nature of the problem, it considers three alternative interpretations (Humean, postmodern and Hegelian) of why the problem resists logical solutions and of its significance for social theory. (shrink)

We argue that solving the heterogeneous problems arising from the standard game theory requires looking both at reasoning heuristics, as in Colman's analysis, and at how people represent games and the quantities that define them.

To determine what the speaker in a cooperative dialog meant with his assertion, on top of what he explicitly said, it is crucial that we assume that the assertion he gave was optimal. In determining optimal assertions we assume that dialogs are embedded in decision problems (van Rooij 2003) and use backwards induction for calculating them (Benz 2006). In this paper, we show that in terms of our framework we can account for several types of implicatures in a uniform way, (...) suggesting that there is no need for an independent linguistic theory of generalized implicatures. In the final section, we show how we can embed our theory in the framework of signaling games, and how it relates with other game theoretic analyses of implicatures. (shrink)

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like rationality at a node and knowledge at a node. We distinguish between the game theorist's and the players' own theory of the game. The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the (...) game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory. (shrink)

The Common Prior Assumption (CPA) is central to the economics of information and the foundations of game theory. Recent contributions (Dekel and Gul, 1997, Gul, 1996, Lipman, 1995) have questioned its meaningfulness in situations of incomplete information where there is no ex ante stage and the primitives of the model are the individuals’ belief hierarchies. We address this conceptual issue by providing characterizations of two local versions of the CPA which are in terms of the primitives and, therefore, do not (...) involve a counterfactual and problematic ex ante stage. The characterizations involve three notions: Comprehensive Agreement, no error of beliefs and common belief in no error. Comprehensive Agreement is defined as the absence of “agreement to disagree” about any aspect of beliefs; it is a generalization of Aumann’s (1976) notion of agreement. The entire analysis is carried out locally, that is, with reference to the “true state” (which represents the actual profile of belief hierarchies) and does not rely on the Truth Axiom for individual beliefs. (shrink)

We develop an analysis of discourse anaphora—the relationship between a pronoun and an antecedent earlier in the discourse—using games of partial information. The analysis is extended to include information from a variety of different sources, including lexical semantics, contrastive stress, grammatical relations, and decision theoretic aspects of the context.

David Lewis is widely credited with the first formulation of common knowledge and the first rigorous analysis of convention. However, common knowledge and convention entered mainstream game theory only when they were formulated, later and independently, by other theorists. As a result, some of the most distinctive and valuable features of Lewis' game theory have been overlooked. We re-examine this theory by reconstructing key parts in a more formal way, extending it, and showing how it differs from more recent game (...) theory. In contrast to current theories of common knowledge, Lewis' theory is based on an explicit analysis of the modes of reasoning that are accessible to rational individuals and so can be used to analyse the genesis of common knowledge. Lewis' analysis of convention emphasises the role of inductive reasoning and of salience in the maintenance of conventions over time. Footnotes Earlier versions of this paper were presented at the 13th Amsterdam Colloquium at the University of Amsterdam, at a workshop on social norms at Wissenschaftskolleg zu Berlin, and at seminars at Tilburg University and the University of Bristol. We are grateful for comments from participants at those meetings, from two anonymous referees, and from Michael Bacharach, Nick Bardsley, Cristina Bicchieri, Luc Bovens, Simon Grant, David McCarthy, Shepley Orr, Brian Skyrms, Peter Vanderschraaf, Peter Wakker and Jörgen Weibull. Robert Sugden's work was supported by the Leverhulme Trust. (shrink)

We develop a logical system that captures two different interpretations of what extensive games model, and we apply this to a long-standing debate in game theory between those who defend the claim that common knowledge of rationality leads to backward induction or subgame perfect (Nash) equilibria and those who reject this claim. We show that a defense of the claim à la Aumann (1995) rests on a conception of extensive game playing as a one-shot event in combination with a principle (...) of rationality that is incompatible with it, while a rejection of the claim à la Reny (1988) assumes a temporally extended, many-moment interpretation of extensive games in combination with implausible belief revision policies. In addition, the logical system provides an original inductive and implicit axiomatization of rationality in extensive games based on relations of dominance rather than the usual direct axiomatization of rationality as maximization of expected utility. (shrink)

While fairness is often mentioned as a determinant of ultimatum bargaining behavior, few data sets are available that can test theories that incorporate fairness considerations. This paper tests the reciprocal kindness theory in Rabin (1993 Incorporating fairness into game theory and economics, The American Economic Review 83: 1281-1302) as an application to the one-period ultimatum bargaining game. We report on data from 100 ultimatum games that vary the financial stakes of the game from 1 to 15. Responder behavior is strongly (...) in support of the kindness theory and proposer behavior weakly in support of it. Offer percentages and past offers influence behavior the most, whereas the size of the pie has a marginally significant effect on offer percentages. The data is more in support of reciprocal kindness than alternative theories of equal-split or learning behavior, although the data also weakly support a minimum percentage threshold hypothesis. As a whole, our results together with existing studies suggest that, for smaller stakes games, fairness considerations dominate monetary considerations. This has implications for more complicated naturally occurring bargaining environments in which the financial stakes can vary widely. (shrink)

The paper presents a variation of the EMAIL Game, originally proposed byRubinstein (American Economic Review, 1989), in which coordination ofthe more rewarding-risky joint course of actions is shown to obtain, evenwhen the relevant game is, at most, ``mutual knowledge.'' In the exampleproposed, a mediator is introduced in such a way that two individualsare symmetrically informed, rather than asymmetrically as in Rubinstein,about the game chosen by nature. As long as the message failure probabilityis sufficiently low, with the upper bound being a (...) function of the gamepayoffs, conditional beliefs in the opponent's actions can allow playersto choose a more rewarding-risky action. The result suggests that, forefficient coordination to obtain, the length of interactive knowledge onthe game, possibly up to ``almost common knowledge,'' does not seem to bea major conceptual issue and that emphasis should be focused instead onthe communication protocol and an appropriate relationship between thereliability of communication channels and the payoffs at stake. (shrink)

The mechanisms/abilities of agents compared to the emergent outcomes in three different scenarios from my past work is summarised: the El Farol Game; an Artificial Stock Market; and the Iterated Prisoner’s Dilemma. Within each of these, the presence or absence of some different agent abilities was examined, the results being summarised here – some turning out to be necessary, some not. The ability in terms of the recognition of other agents, either by characteristics or by name is a recurring theme. (...) Some of the difficulties in reaching a systematic understanding of these connections is briefly discussed. (shrink)

A feature of David Lewis's account of conventions in his book "Convention" which has received admiring notices from philosophers is his use of the mathematical theory of games. In this paper I point out a number of serious flaws in Lewis's use of game theory. Lewis's basic claim is that conventions cover 'coordination problems'. I show that game-Theoretical analysis tends to establish that coordination problems in Lewis's sense need not underlie conventions.

We extend previous work on cooperation to some related questions regarding the evolution of simple forms of communication. The evolution of cooperation within the iterated Prisoner's Dilemma has been shown to follow different patterns, with significantly different outcomes, depending on whether the features of the model are classically perfect or stochastically imperfect (Axelrod 1980a, 1980b, 1984, 1985; Axelrod and Hamilton, 1981; Nowak and Sigmund, 1990, 1992; Sigmund 1993). Our results here show that the same holds for communication. Within a simple (...) model, the evolution of communication seems to require a stochastically imperfect world. (shrink)

We continue the work initiated in Herzig and Lorini (J Logic Lang Inform, in press) whose aim is to provide a minimalistic logical framework combining the expressiveness of dynamic logic in which actions are first-class citizens in the object language, with the expressiveness of logics of agency such as STIT and logics of group capabilities such as CL and ATL. We present a logic called ( Deterministic Dynamic logic of Agency ) which supports reasoning about actions and joint actions of (...) agents and coalitions, and agentive and coalitional capabilities. In it is supposed that, once all agents have selected a joint action, the effect of this joint action is deterministic. In order to assess we prove that it embeds Coalition Logic. We then extend with modal operators for agents’ preferences, and show that the resulting logic is sufficiently expressive to capture the game-theoretic concepts of best response and Nash equilibrium. (shrink)

The importance of the notion of common knowledge in sustaining cooperative outcomes in strategic situations is well appreciated. However, the systematic analysis of the extent to which small departures from common knowledge affect equilibrium in games has only recently been attempted.We review the main themes in this literature, in particular, the notion of common p-belief. We outline both the analytical issues raised, and the potential applicability of such ideas to game theory, computer science and the philosophy of language.

Recently, natural language pragmatics started to make use of decision-, game-, and information theoretical tools to determine the usefulness of questions and assertions in a quantitative way. In the first part of this paper several of these notions are related with each other. It is shown that under particular natural assumptions the utility of questions and answers reduces to their informativity, and that the ordering relation induced by utility sometimes even reduces to the logical relation of entailment. The second part (...) of the paper shows how different proposals (using either protocols or likelihood functions) to measure the relevance/utility of non-partitional questions come down to the same thing. (shrink)

The paper begins by providing a game-theoretic reconstruction of Gilbert’s (1989) philosophical critique of Lewis (1969) on the role of salience in selecting conventions. Gilbert’s insight is reformulated thus: Nash equilibrium is insufficiently powerful as a solution concept to rationalize conventions for unboundedly rational agents if conventions are solutions to the kinds of games Lewis supposes. Both refinements to NE and appeals to bounded rationality can plug this gap, but lack generality. As Binmore (this issue) argues, evolutive game theory readily (...) explains the origin of conventional behavior, but that is not Lewis’s project. Gilbert’s critique is generalized by reference to Bacharach’s (2006) work on team reasoning in games. The paper then argues that although Lewis’s account of the rationalization of conventions is shown by the reconstruction of Gilbert’s critique to be incomplete, Gilbert is wrong to conclude that classical (‘eductive’) game theory lacks the resources to explain conformity to conventions among people. A game-theoretic account of the dynamics of socialization, based on Ross’s (2005, 2006) idea of ‘game determination’, rationalizes choices of conventional strategies in overlapping generations contexts, provided agents are products of evolutionary selection and know that other players are also such products. (shrink)

This paper uses game theory to try to provide a rational grounding for simple pragmatic inferences, scalar implicatures.

This paper offers a novel ‘changing places’ account of identification in games, where the consequences of role swapping are crucial. First, it illustrates how such an account is consistent with the view, in classical game theory, that only outcomes (and not pathways) are significant. Second, it argues that this account is superior to the ‘pooled resources’ alternative when it comes to dealing with some situations in which many players identify. Third, it shows how such a ‘changing places’ account can be (...) used in games where some of the players identify with one another, but others do not. Finally, it illustrates how the model can handle the notion that identification comes in degrees. (shrink)

The partial cooperation displayed by subjects in the Centipede Game deviates radically from the predictions of traditional game theory. Even standard, infinite population, evolutionary settings have failed to provide an explanation for this behavior. However, recent work in finite population evolutionary models has shown that such settings can produce radically different results from the standard models. This paper examines the evolution of partial cooperation in finite populations. The results reveal a new possible explanation that is not open to the standard (...) models and gives us reason to be cautious when employing these otherwise helpful idealizations. *Received January 2007; revised November 2007. †To contact the author, please write to: Department of Logic and Philosophy of Science, University of California, 3151 Social Science Plaza A, Irvine, CA 92697-5100; e-mail: rsmead@uci.edu. (shrink)

In one-shot public goods dilemmas, defection is the strictly dominant strategy. However, agents with cooperative strategies can do well if (1) agents are `translucent' (that is, if agents can fallibly recognize the strategy other agents play ex ante ) and (2) an institutional structure allows `assortation' such that cooperative agents can increase the likelihood of playing with their own kind. The model developed in this article shows that even weak levels of translucency suffice if cooperators are able to pool their (...) information to exclude defectors. Computer simulations confirm this claim. The results imply that conditional cooperation can be a successful strategy given translucency and `assortation', even if the game has a one-shot character. The article discusses implications for moral theory against the backdrop of `virtual self-regard' and the concept of moral integrity. Key Words: public good • game theory • prisoner's dilemma • translucency • assortation • group formation • group identity • integrity • altruism. (shrink)

Abstract Orthodox decision theory presupposes that agency is invested in individuals. An opposing literature allows team agency to be invested in teams whose members use distinctive modes of team reasoning. This paper offers a new conceptual framework, inspired by David Lewis's analysis of common reasons for belief, within which team reasoning can be represented. It shows how individuals can independently endorse a principle of team reasoning which prescribes acting as a team member conditional on assurance that others have endorsed the (...) same principle. It argues that there can be such assurance even when no individual has an obligation to act on team reasoning. *This paper originated in a lecture that I gave at a Colloquium on Collective Intentions at Erasmus University Rotterdam. I thank participants, and particularly Govert den Hartogh, for comments. The analysis presented in this paper is an offshoot of a larger project, which uses David Lewis's work as the starting point for a reconstruction of the foundations of game theory. That project is joint work with Robin Cubitt. The specific idea of using this approach to analyse team reasoning grew out of a discussion with Michael Bratman. My work was supported by the Leverhulme Trust. (shrink)

Individual rational action consists of (i) knowing what you want, (ii) taking proper steps to approach what you want as closely as possible, within the confines of the law. This one can learn, although some people are more skilled in it than others. Modern democracies are set up in such a way that they leave as much room as possible for individual rational action. Education for citizenship is sometimes taken to be: getting young citizens acquainted with the legal possibilities for (...) maximizing their individual interests. How about collective rational action? Game theory shows that if people engage in individual rational action, the common good suffers. This is known as ‘the tragedy of the commons’. It was also known in Antiquity: ”What is common to the greatest number has the least care bestowed upon it” (Aristotle). To understand the issues involved we will analyse the notions of ”common knowledge”, ”individual commitment” and ”collective intention”. (shrink)

Recently, natural language pragmatics started to make use of decision-, game-, and information theoretical tools to determine the usefulness of questions and assertions in a quantitative way. In the first part of this paper several of these notions are related with each other. It is shown that under particular natural assumptions the utility of questions and answers reduces to their informativity, and that the ordering relation induced by utility sometimes even reduces to the logical relation of entailment. The second part (...) of the paper shows how different proposals (using either protocols or likelihood functions) to measure the relevance/utility of non-partitional questions come down to the same thing. (shrink)

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. (shrink)

Recent years have seen increased interest in the question of whether it is possible to provide an evolutionary game theoretic explanation for certain kinds of social norms. These explanatory approaches often rely on the fact that, in certain evolutionary models, the basin of attraction of "fair" or "just" strategies occupies a certain percentage of the state space. I sketch a proof of a general representation theorem for a large class of evolutionary game theoretic models played on a social network, in (...) the hope that this will contribute to a greater understanding of the basins of attraction of such models -- and hence the evolution of social norms. More precisely, I show how many kinds of social networks can be translated into random boolean networks. The interesting and useful part of this result is that, for many social networks, one can find a bijection $f$ between the state space of the social network and the state space of the random boolean network, such that the state $S`$ follows the state $S$ under the dynamical laws of the social network if and only if $f(S`)$ follows the state $f(S)$ under the dynamics of the random boolean network. In some cases, it is not possible to find such a bijection; in these cases, one can find an injection $f$ with the property that if $S`$ follows $S$ under the dynamics of the social network, then $f(S`)$ follows $f(S)$ under the dynamics of the random boolean network. I then use this method to catalog all the basins of attraction for some simple two-strategy games (the prisoner`s dilemma and the stag hunt) played on a ring, drawing on the work of Wuensche and Lesser (1992). (shrink)

Human beings are peculiar. In laboratory experiments, they often cooperate in one-shot prisoners’ dilemmas, they frequently offer 1/2 and reject low offers in the ultimatum game, and they often bid 1/2 in the game of divide-the-cake All these behaviors are puzzling from the point of view of game theory. The first two are irrational, if utility is measured in a certain way.1 The last isn’t positively irrational, but it is no more rational than other possible actions, since there are infinitely (...) many other Nash equilibria besides the one in which both players bid 1/2. At the same time, these behaviors seem to indicate that people are sometimes inclined to be cooperative, fair, and just. In his stimulating new book, Brian Skyrms sets himself the task of showing why these inclinations evolved, or how they might have evolved, under the pressure of natural selection. The goal is not to justify our ethical intuitions, but to explain why we have them.2.. (shrink)

We compare Colman's proposed “psychological game theory” with the existing literature on psychological games (Geanakoplos et al. 1989), in which beliefs and intentions assume a prominent role. We also discuss experimental evidence on intentions, with a particular emphasis on reciprocal behavior, as well as recent efforts to show that such behavior is consistent with social evolution.

A fundamental philosophical question that arises in connection with evolutionary theory is whether the fittest patterns of behavior are always the most rational. Are fitness and rationality fully compatible? When behavioral rationality is characterized formally as in classical decision theory, the question becomes mathematically meaningful and can be explored systematically by investigating whether the optimally fit behavior predicted by evolutionary process models is decision-theoretically coherent. Upon investigation, it appears that in nontrivial evolutionary models the expected behavior is not always in (...) accord with the norms of the standard theory of decision as ordinarily applied. Many classically irrational acts, e.g. betting on the occurrence of one event in the knowledge that the probabilities favor another, can under certain circumstances constitute adaptive behavior.One interesting interpretation of this clash is that the criterion of rationality offered by classical decision theory is simply incorrect (or at least incomplete) as it stands, and that evolutionary theory should be called upon to provide a more generally applicable theory of rationality. Such a program, should it prove feasible, would amount to the logical reduction of the theory of rational choice to evolutionary theory. (shrink)

Using a simple learning agent, we show that learning self-control in the primrose path experiment does parallel learning cooperation in the prisoner's dilemma. But Rachlin's claim that “there is no essential difference between self-control and altruism” is too strong. Only iterated prisoner's dilemmas played against reciprocators are reduced to self-control problems. There is more to cooperation than self-control and even altruism in a strong sense.

This collection focuses on questions that arise when morality is considered from the perspective of recent work on rational choice and evolution. Linking questions like "Is it rational to be moral?" to the evolution of cooperation in "The Prisoners Dilemma," the book brings together new work using models from game theory, evolutionary biology, and cognitive science, as well as from philosophical analysis. Among the contributors are leading figures in these fields, including David Gauthier, Paul M. Churchland, Brian Skyrms, Ronald de (...) Sousa, and Elliot Sober. (shrink)

The importance of applying game theory to the evolution of information in the presence of noise has recently become widely recognized. This Special Issue addresses the theme of spontaneously emergent order in both classical and quantum systems subject to external noise, and includes papers directly related to game theory or the development of supporting techniques. In the following editorial overview we examine the broader context of the subject, including the tension between the destructive and creative aspects of noise, and foreshadow (...) the significance of some of the subsequent papers in the volume. (shrink)

Game theory is the mathematical study of strategy and conflict. It has wide applications in economics, political science, sociology, and, to some extent, in philosophy. Where rational choice theory or decision theory is concerned with individual agents facing games against nature, game theory deals with games in which all players have preference orderings over the possible outcomes of the game. This paper gives an informal introduction to the theory and a survey of applications in diverse branches of philosophy. No criticism (...) is reviewed. Game theory is shown at work in discussions about epistemological dependence (prisoner’s dilemma), liberalism and efficiency (Nash equilibrium), Hume’s concept of convention (correlated equilibrium), morality and rationality (bargaining games), and distributive justice and egalitarianism (evolutionary game theory). A guide to the literature provides hints at applications in collective intentionality, epistemology, ethics, history of philosophy, logic, philosophy of language, and political philosophy. (shrink)

The computer simulation study explores the impact of the duration of social impact on the generation and stabilization of cooperative strategies. Rather than seeding the simulations with a finite set of strategies, a continuous distribution of strategies is being defined. Members of heterogeneous populations were characterized by a pair of probabilistic reactive strategies: the probability to respond to cooperation by cooperation and the probability to respond to defection by cooperation. This generalized reactive strategy yields the standard TFT mechanism, the All-Cooperate, (...) All-Defect and Bully strategies as special cases. Pairs of strategies interacted through a Prisoner's Dilemma game and exerted social influence on all other members. Manipulating: (i) the initial distribution of populations' strategies, and (ii) the duration of social influence, we monitored the conditions leading to the emergence and stabilization of cooperative strategies. Results show that: (1) The duration of interactions between pairs of strategies constitutes a crucial factor for the emergence and stabilization of cooperative strategies, (2) Unless sufficient learning intervals are provided, initializing the simulations with cooperative populations does not guarantee that cooperation will sustain. (shrink)

Human beings are peculiar. In laboratory experiments, they often cooperate in one-shot prisoners’ dilemmas, they frequently offer 1/2 and reject low offers in the ultimatum game, and they often bid 1/2 in the game of divide-the-cake All these behaviors are puzzling from the point of view of game theory. The first two are irrational, if utility is measured in a certain way.1 The last isn’t positively irrational, but it is no more rational than other possible actions, since there are infinitely (...) many other Nash equilibria besides the one in which both players bid 1/2. At the same time, these behaviors seem to indicate that people are sometimes inclined to be cooperative, fair, and just. In his stimulating new book, Brian Skyrms sets himself the task of showing why these inclinations evolved, or how they might have evolved, under the pressure of natural selection. The goal is not to justify our ethical intuitions, but to explain why we have them.2.. (shrink)

We extend previous work on cooperation to some related questions regarding the evolution of simple forms of communication. The evolution of cooperation within the iterated Prisoner's Dilemma has been shown to follow different patterns, with significantly different outcomes, depending on whether the features of the model are classically perfect or stochastically imperfect (Axelrod 1980a, 1980b, 1984, 1985; Axelrod and Hamilton, 1981; Nowak and Sigmund, 1990, 1992; Sigmund 1993). Our results here show that the same holds for communication. Within a simple (...) model, the evolution of communication seems to require a stochastically imperfect world. (shrink)

Robustness has long been recognized as an important parameter for evaluating game-theoretic results, but talk of ‘robustness’ generally remains vague. What we offer here is a graphic measure for a particular kind of robustness (‘matrix robustness’), using a three-dimensional display of the universe of 2 × 2 game theory. In such a measure specific games appear as specific volumes (Prisoner’s Dilemma, Stag Hunt, etc.), allowing a graphic image of the extent of particular game-theoretic effects in terms of those games. The (...) measure also allows for an easy comparison between different effects in terms of matrix robustness. Here we use the measure to compare the robustness of Tit for Tat’s well-known success in spatialized games (Axelrod, R. (1984). The evolution of cooperation. New York: Basic Books; Grim, P. et al. (1998). The philosophical computer: Exploratory essays in philosophical computer modeling. Cambridge, Mass: MIT Press) with the robustness of a recent game-theoretic model of the contact hypothesis regarding prejudice reduction (Grim et al. 2005. Public Affairs Quarterly, 19, 95–125). (shrink)

This paper contributes to the explanation of human cooperative behaviour, examining the implications of Brian Skyrms’ modelling of the prisoner’s dilemma (PD). Augmenting a PD with signalling strategies promotes cooperation, but a challenge that must be addressed is what prevents signals being subverted by deceptive behaviour. Empirical results suggest that emotional displays can play a signalling role and, to some extent, are secure from subversion. I examine proximate explanations and then offer an evolutionary explanation for the translucency of emotional displays. (...) Selection acts on the basis of lifetime fitness consequences and, crucially for my argument, the intensity of selection decreases over the course of a lifetime. Hence we tend to possess traits that promote survival when young and, with regard to emotional displays, translucency allows successful maturation over our protracted period of nurturing by close kin. This is due to the vital role played by emotional interactions in the normal cognitive and social development of Homo sapiens. (shrink)

John Maynard Smith was the founder of evolutionary game theory. He has also been the major influence on the direction of this field, which now pervades behavioural ecology and evolutionary biology. In its original formulation the theory had three components: a set of strategies, a payoff structure, and a concept of evolutionary stability. These three key components are still the basis of the theory, but what is assumed about each component is often different to the original assumptions. We review modern (...) approaches to these components. We emphasis that if a game is considered in isolation, and arbitrary payoffs are assumed, then the payoffs may not be consistent with other components of the system which are not modelled. Modelling the whole system, including not only the focal game, but also the future behaviour of the players and the behaviour of other population members, allows a consistent model to be constructed. We illustrate this in the case of two models of parental care, showing how linking a focal game to other aspects of the system alters what is predicted. (shrink)

Individualism fixes the unit of rational agency at the individual, creating problems exemplified in Hi-Lo and Prisoner's Dilemma (PD) games. But instrumental evaluation of consequences does not require a fixed individual unit. Units of agency can overlap, and the question of which unit should operate arises. Assuming a fixed individual unit is hard to justify: It is natural, and can be rational, to act as part of a group rather than as an individual. More attention should be paid to how (...) units of agency are formed and selected: Are the local processes local or nonlocal? Do they presuppose the ability to understand other minds? (shrink)

We consider the Stag Hunt in terms of Maynard Smith’s famous Haystack model. In the Stag Hunt, contrary to the Prisoner’s Dilemma, there is a cooperative equilibrium besides the equilibrium where every player defects. This implies that in the Haystack model, where a population is partitioned into groups, groups playing the cooperative equilibrium tend to grow faster than those at the non-cooperative equilibrium. We determine under what conditions this leads to the takeover of the population by cooperators. Moreover, we compare (...) our results to the case of an unstructured population and to the case of the Prisoner’s Dilemma. Finally, we point to some implications our findings have for three distinct ideas: Ken Binmore’s group selection argument in favor of the evolution of efficient social contracts, Sewall Wright’s Shifting Balance theory, and the equilibrium selection problem of game theory. (shrink)

David Gauthier claims that it can be rational to co-operate in a prisoner's dilemma if one has adopted a disposition constraining one's self from maximizing one's individual expected utility, i.e., a constrained maximizer disposition. But I claim cooperation cannot be both voluntary and constrained. In resolving this tension I ask what constrained maximizer dispositions might be. One possibility is that they are rationally acquired, irrevocable psychological mechanisms which determine but do not rationalize cooperation. Another possibility is that they are rationally (...) acquired preference-functions rationalizing cooperation as maximizing. I argue that if they are the first thing, then their adoption fails to make co-operation rational even if, as Gauthier also claims, actions are rational if they express rational dispositions. I then suggest that taking constrained maximizer dispositions to be things of the second sort would result in them being able to make co-operation rational, and that so-taking them therefore serves the bulk and spirit of Gauthier's larger claims, which I reconstruct accordingly. (shrink)

Hamilton games-theoretic conflict model, which applies Maynard Smith's concept of evolutionarily stable strategy to the Prisoner's Dilemma, gives rise to an inconsistency between theoretical prescription and empirical results. Proposed resolutions of thisproblem are incongruent with the tenets of the models involved. The independent consistency of each model is restored, and the anomaly thereby circumvented, by a proof that no evolutionarily stable strategy exists in the Prisoner's Dilemma.

Recent years have seen increased interest in the question of whether it is possible to provide an evolutionary game-theoretic explanation for certain kinds of social norms. I sketch a proof of a general representation theorem for a large class of evolutionary game-theoretic models played on a social network, in hope that this will contribute to a greater understanding of the long-term evolutionary dynamics of such models, and hence the evolution of social norms.

In models of multi-level selection, the property of Darwinian fitness is attributed to entities at more than one level of the biological hierarchy, e.g. individuals and groups. However, the relation between individual and group fitness is a controversial matter. Theorists disagree about whether group fitness should always, or ever, be defined as total (or average) individual fitness. This paper tries to shed light on the issue by drawing on work in social choice theory, and pursuing an analogy between fitness and (...) utility. Social choice theorists have long been interested in the relation between individual and social utility, and have identified conditions under which social utility equals total (or average) individual utility. These ideas are used to shed light on the biological problem. (shrink)

Robustness has long been recognized as an important parameter for evaluating game-theoretic results, but talk of ‘robustness’ generally remains vague. What we offer here is a graphic measure for a particular kind of robustness (‘matrix robustness’), using a three-dimensional display of the universe of 2 × 2 game theory. In such a measure specific games appear as specific volumes (Prisoner’s Dilemma, Stag Hunt, etc.), allowing a graphic image of the extent of particular game-theoretic effects in terms of those games. The (...) measure also allows for an easy comparison between different effects in terms of matrix robustness. Here we use the measure to compare the robustness of Tit for Tat’s well-known success in spatialized games (Axelrod, R. (1984). The evolution of cooperation . New York: Basic Books; Grim, P. et al. (1998). The philosophical computer: Exploratory essays in philosophical computer modeling . Cambridge, Mass: MIT Press) with the robustness of a recent game-theoretic model of the contact hypothesis regarding prejudice reduction (Grim et al. 2005. Public Affairs Quarterly, 19 , 95–125). (shrink)

The article investigates the interplay of moral rules in computer simulation. The investigation is based on two situations which are well-known to game theory: the prisoner''s dilemma and the game of Chicken. The prisoner''s dilemma can be taken to represent contractual situations, the game of Chicken represents a competitive situation on the one hand and the provision for a common good on the other. Unlike the rules usually used in game theory, each player knows the other''s strategy. In that way, (...) ever higher levels of reflection are reached reciprocally. Such strategies can be interpreted as moral rules.Artificial morality is related to the discipline of Artificial Life. As in artificial life, the use of genetic algorithms suggests itself. Rules of behaviour split and reunite as chromosome strings do. (shrink)

Jan Österberg (Self and Others, 1988) argues that the most defensible form of egoism should not only tell each of us what to do but also tell us what we ought to do. He also claims that collective norms should take precedence over individual ones. An individual ought to do one's part in an action pattern that is prescribed for the group - provided that other members of the group do their part. question This paper questions Österberg's claim that Collective (...) Egoism, unlike other forms of egoism, avoids violations of the principles which he takes to be analytical adequacy criteria for ethical theories: the principles of "deontic consequence" and "joint satisfiability". Furthermore, it questions his argument that Collective Egoism yields the "right" prescriptions in its main test-case: Prisoners' Dilemma. The improved version of Collective Egoism is able to deal with the two-person Prisoners' Dilemma, but it still misbehaves when we move to the many-persons cases. A certain type of "free rider"-problems proves to be especially troublesome. (shrink)

Abstract Daniel Dennett advocates the use of the intentional stance in adaptationist biology and in cognitive ethology. He sees intentional system theory as closely related to decision theory and game theory. In biological decision and game theory models, nature ?chooses? the strategy by which the animal chooses a course of action. The design of the animal imposes constraints on the model. For Dennett, by contrast, the description of nature's rationale imposes constraints on the design of the animal. Dennett's oversimplified conception (...) of nature's rationale undermines the usefulness of the intentional stance as a tool in cognitive ethology. Intentional system theory can be made more useful in investigating animal cognition by modifying its application to questions of biological function. (shrink)

Game theory has played a critical role in elucidating the evolutionary origins of social behavior. Sober and Wilson (1999) model altruism as a prisoner's dilemma and claim that this model indicates that altruism arose from group selection pressures. Sober and Wilson also suggest that the prisoner's dilemma model can be used to characterize punishment; hence, punishment too originated from group selection pressures. However, empirical evidence suggests that a group selection model of the origins of altruistic punishment may be insufficient. I (...) argue that examining dominance hierarchies and coalition formation in chimpanzee societies suggests that the origins of altruistic punishment may be best captured by individual selection models. I suggest that this shows the necessity of coupling of game-theoretic models with a conception of what our actual social structure may have been like to best model the origins of our own behavior. ‡I would like to thank Zachary Ernst and Emma Marris for their many helpful comments which greatly improved this paper. †To contact the author, please write to: Department of Philosophy, University of Maryland, Skinner Building, College Park, MD 20742; e-mail: yrohwer@umd.edu. (shrink)

This paper considers whether the available evidence from archeology, biological anthropology, primatology, and comparative gene-sequencing, can test evolutionary game theory models of cooperation as historical hypotheses about the actual course of human prehistory. The examination proceeds on the assumption that cooperation is the product of cultural selection and is not a genetically encoded trait. Nevertheless, we conclude that gene sequence data may yet shed significant light on the evolution of cooperation.

In this article, I critically respond to Herbert Gintis's criticisms of the behavioral-economic foundations of Ken Binmore's game-theoretic theory of justice. Gintis, I argue, fails to take full account of the normative requirements Binmore sets for his account, and also ignores what I call the ‘scale-relativity’ considerations built into Binmore's approach to modeling human evolution. Paul Seabright's criticism of Binmore, I note, repeats these oversights. In the course of answering Gintis's and Seabright's objections, I clarify and (...) extend Binmore's theory in a number of respects, integrating it with Kim Sterelny's and Don Ross's recent (respective) work on the evolution of people as cultural entities. The account also yields a novel basis for choosing between socialism (broadly conceived) and what Binmore calls ‘whiggery’ as normative political programs. Key Words: theory of justice • bargaining theory • evolutionary game theory • human evolution • Ken Binmore • Herbert Gintis • Kim Sterelny. (shrink)

The proper treatment of correlation in evolutionary game theory has unexpected connections with recent philosophical discussions of the theory of rational decision. The Logic of Decision (Jeffrey 1983) provides the correct framework for correlated evolutionary game theory and a variant of "ratifiability" is the appropriate generalization of "evolutionarily stable strategy". The resulting theory unifies the treatment of correlation due to kin, population viscosity, detection, signaling, reciprocal altruism, and behavior-dependent contexts. It is shown that (1) a strictly dominated strategy may be (...) selected, and (2) under conditions of perfect correlation a strictly efficient strategy must be selected. (shrink)

Biologists rely extensively on the iterated Prisoner's Dilemma game to model reciprocal altruism. After examining the informal conditions necessary for reciprocal altruism, I argue that formal games besides the standard iterated Prisoner's Dilemma meet these conditions. One alternate representation, the modified Prisoner's Dilemma game, removes a standard but unnecessary condition; the other game is what I call a Cook's Dilemma. We should explore these new models of reciprocal altruism because they predict different stability characteristics for various strategies; for instance, I (...) show that strategies such as Tit-for-Tat have different stability dynamics in these alternate models. (shrink)

I shall introduce the units 0f decision problem in thc theory of decision, which as I shall explain is 21 sibling t0 thc units 0f selection problem in cvolutionary thcory. And I shall present an argument to thc cffcct that, contrary to Bayesian wisdom on the subject, undertaking decision in group settings (in multi-individual units) violates no precepts of rationality.

In this paper we revise Reinforcement Learning and adaptiveness in Multi-Agent Systems from an Evolutionary Game Theoretic perspective. More precisely we show there is a triangular relation between the fields of Multi-Agent Systems, Reinforcement Learning and Evolutionary Game Theory. We illustrate how these new insights can contribute to a better understanding of learning in MAS and to new improved learning algorithms. All three fields are introduced in a self-contained manner. Each relation is discussed in detail with the necessary background information (...) to understand it, along with major references to relevant work. (shrink)

Peter Vanderschraaf. Game Theory, Evolution and Justice.

A computer simulation runs a model generating a phenomenon under investigation. For the simulation to be explanatory, the model has to be explanatory. The model must be isomorphic to the natural system that realizes the phenomenon. This paper elaborates the method of assessing a simulation's explanatory power. Then it illustrates the method by applying it to two simulations in game theory. The first is Brian Skyrms's (1990) simulation of interactive deliberations. It is intended to explain the emergence of a Nash (...) equilibrium in a noncooperative game. The second is Skyrms's (2004) simulation of the evolution of cooperation. It is intended to explain cooperation in assurance games. The final section suggests ways of enhancing the explanatory power of these simulations. (shrink)

My aim in this paper is to demonstrate that a very simple learning rule based on imitation can help to sustain altruism as a culturally transmitted pattern or behaviour among agents playing a standard prisoner’s dilemma game. The point of this demonstration is not to prove that imitation is single-handedly responsible for existing levels of altruism (a thesis that is false), nor is the point to show that imitation is an important factor in explanations for the evolution of altruism (a (...) thesis already prominent in the existing literature). The point is to show that imitation contributes to the evolution of altruism in a particular way that is not always fairly represented by evolutionary game theory models. Specifically, the paper uses a simple model to illustrate that cultural transmission includes mechanisms that do not transmit phenotype vertically (i.e. from parent to related offspring) and that these mechanisms can promote altruism in the absence of any direct biological propensity favouring such behaviour. This is a noteworthy result because it shows that evolutionary models can be built to explicitly reflect the contribution of non-vertical transmission in our explanations for the evolution of altruism among humans and other social species. (shrink)

Kin selection, reciprocity and group selection are widely regarded as evolutionary mechanisms capable of sustaining altruism among humans andother cooperative species. Our research indicates, however, that these mechanisms are only particular examples of a broader set of evolutionary possibilities.In this paper we present the results of a series of simple replicator simulations, run on variations of the 2–player prisoner's dilemma, designed to illustrate the wide range of scenarios under which altruism proves to be robust under evolutionary pressures. The set of (...) mechanisms we explore is divided into four categories:correlation, group selection, imitation, and punishment. We argue that correlation is the core phenomenon at work in all four categories. (shrink)