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)