The iterated prisoner’s dilemma (IPD) has been widely used in the biological and social sciences to model dyadic cooperation. While most of this work has focused on the discrete prisoner’s dilemma, in which actors choose between cooperation and defection, there has been some analysis of the continuous IPD, in which actors can choose any level of cooperation from zero to one. Here, we analyse a model of the continuous IPD with a limited strategy set, and show that a generous strategy (...) achieves the maximum possible payoff against its own type. While this strategy is stable in a neighborhood of the equilibrium point, the equilibrium point itself is always vulnerable to invasion by uncooperative strategies, and hence subject to eventual destabilization. The presence of noise or errors has no effect on this result. Instead, generosity is favored because of its role in increasing contributions to the most efficient level, rather than in counteracting the corrosiveness of noise. Computer simulation using a single-locus infinite alleles Gaussian mutation model suggest that outcomes ranging from a stable cooperative polymorphism to complete collapse of cooperation are possible depending on the magnitude of the mutational variance. Also, making the cost of helping a convex function of the amount of help provided makes it more difficult for cooperative strategies to invade a non-cooperative equilibrium, and for the cooperative equilibrium to resist destabilization by noncooperative strategies. (shrink)

1 Background for the Uninitiated RICHMOND CAMPBELL Paradoxes are intrinsically fascinating. They are also distinctively ...

The backward induction argument purports to show that rational and suitably informed players will defect throughout a finite sequence of prisoner's dilemmas. It is supposed to be a useful argument for predicting how rational players will behave in a variety of interesting decision situations. Here, I lay out a set of assumptions defining a class of finite sequences of prisoner's dilemmas. Given these assumptions, I suggest how it might appear that backward induction succeeds and why it is actually fallacious. Then, (...) I go on to consider the consequences of adopting a stronger set of assumptions. Focusing my attention on stronger sets that, like the original, obey the informedness condition, I show that any supplementation of the original set that preserves informedness does so at the expense of forcing rational participants in prisoner's dilemma situations to have unexpected beliefs, ones that threaten the usefulness of backward induction. (shrink)

Existing models of strategic decision making typically assume that only the attributes of the currently played game need be considered when reaching a decision. The results presented in this article demonstrate that the so-called “cooperativeness” of the previously played prisoner’s dilemma games influence choices and predictions in the current prisoner’s dilemma game, which suggests that games are not considered independently. These effects involved reinforcement-based assimilation to the previous choices and also a perceptual contrast of the present game with preceding games, (...) depending on the range and the rank of their cooperativeness. A. Parducci’s (1965) range frequency theory and H. Helson’s (1964) adaptation level theory are plausible theories of relative judgment of magnitude information, which could provide an account of these context effects. (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)

InMorals by Agreement, David Gauthier (1986) argues that it is rational to intend to cooperate, even in single-play Prisoner's Dilemma games, provided (1) your co-player has a similar intention; (2) both intentions can be revealed to the other player. To this thesis four objections are made. (a) In a strategic decision the parameters on which the argument relies cannot be supposed to be given. (b) Of each pair ofa-symmetric intentions at least one is not rational. But it is impossible to (...) form symmetric intentions to cooperate conditionally. For the condition on which the decision depends cannot be fulfilled without deciding. (c) If one's intention has to be ascertained on the basis of information about one's past performance, it is straightforwardly rational to intend to cooperate, but there is no reason to do so in a single-play PD. (d) The argument cannot be extended ton-person games which are Gauthier's principal concern. (shrink)

The aim of this paper is to critically review the game-theoretic discussion of Hobbes and to develop a game-theoretic interpretation that gives due attention both to Hobbes's distinction between “moderates” and “dominators” and to what actually initiates conflict in the state of nature, namely, the competition for vital goods. As can be shown, Hobbes's state of nature contains differently structured situations of choice, the game-theoretic representation of which requires the prisoner's dilemma and the assurance game and the so-called assurance dilemma. (...) However, the “state of war” ultimately emerges from situations that cannot be described by any of these games because they represent zero-sum games in which the outcome of mutual cooperation does not exist. (shrink)

The "Prisoner's Dilemma" game has been extensively discussed in both the public and academic press. Thousands of articles and many books have been written about this disturbing game and its apparent representation of many problems of society. The origin of the game is attributed to Merrill Flood and Melvin Dresher. I quote from the Stanford Encyclopedia of Philosophy: Puzzles with this structure were devised and discussed by Merrill Flood and Melvin Dresher in 1950, as part of the Rand CorporationÂ’s investigations (...) into game theory (which Rand pursued because of possible applications to global nuclear strategy). The title "prisonerÂ’s dilemma" and the version with prison sentences as payoffs are due to Albert Tucker, who wanted to make Flood and DresherÂ’s ideas more accessible to an audience of Stanford psychologists. The Prisoner's Dilemma is a short parable about two prisoners who are individually offered a chance to rat on each other for which the "ratter" would receive a lighter sentence and the "rattee" would receive a harsher sentence. The problem results from the fact that both can play this game -- that is, defect -- and if both do, then both do worse than they would had they both kept silent. This peculiar parable serves as a model of cooperation between two or more individuals (or corporations or countries) in ordinary life in that in many cases each individual would be personally better off not cooperating (defecting) on the other. (shrink)

Gauthier's argument for constrained maximization, presented inMorals by Agreement, is perfected by taking into account the possibility of accidental exploitation and discussing the limitations on the values of the parameters which measure the translucency of the actors. Gauthier's argument is nevertheless shown to be defective concerning the rationality of constrained maximization as a strategic choice. It can be argued that it applies only to a single actor entering a population of individuals who are themselves not rational actors but simple rule-followers. (...) A proper analysis of the strategic choice situation involving two rational actors who confront each other shows that constrained maximization as the choice of both actors can only result under very demanding assumptions. (shrink)

The so-called "Prisoner''s Dilemma" is often referred to in business ethics, but probably not well understood. This article has three parts: (1) I claim that models derived from game theory are significant in the field for discussions of prudential ethics and the practical decisions managers make; (2) I discuss using them as a practical pedagogical exercise and some of the lessons generated; (3) more speculatively, I suggest that they are useful in discussions of corporate personhood.

The Prisoner’s Dilemma is a popular device used by researchers to analyze such institutions as business and the modem corporation. This popularity is not deserved under a certain condition that is widespread in college education. If we, as management educators, take seriouslyour parts in preparing our students to participate in the institutions of a democratic society, then the Prisoner’s Dilemma-as clever a rhetoricaldevice as it is-is an unacceptable means to that end. By posing certain questions about the prisoners in the (...) Prisoner’s Dilemma, I show that management educators have created a Prisoners Dilemma, whereby they intellectually imprison themselves and their students by continuingto appeal to the Prisoner’s Dilemma. These questions are not encouraged by the advocates of the Prisoner’s Dilemma. (shrink)

Collective action is interpreted as a matter of people doing something together, and it is assumed that this involves their having a collective intention to do that thing together. The account of collective intention for which the author has argued elsewhere is presented. In terms that are explained, the parties are jointly committed to intend as a body that such-and-such. Collective action problems in the sense of rational choice theory—problems such as the various forms of coordination problem and the (...) prisoner’s dilemma—are then considered. An explanation is given of how, when such a problem is interpreted in terms of the parties’ inclinations, a suitable collective intention resolves the problem for agents who are rational in a broad sense other than the technical sense of game theory. Key Words: rationality • collective action • collective intention • joint commitment. (shrink)

The primrose path and prisoner's dilemma paradigms may require cognitive (executive) control: The active maintenance of context representations in lateral prefrontal cortex to provide top-down support for specific behaviors in the face of short delays or stronger response tendencies. This perspective suggests further tests of whether altruism is a type of self-control, including brain imaging, induced affect, and dual-task studies.

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)

In the spatialized Prisoner's Dilemma, players compete against their immediate neighbors and adopt a neighbor's strategy should it prove locally superior. Fields of strategies evolve in the manner of cellular automata (Nowak and May, 1993; Mar and St. Denis, 1993a,b; Grim 1995, 1996). Often a question arises as to what the eventual outcome of an initial spatial configuration of strategies will be: Will a single strategy prove triumphant in the sense of progressively conquering more and more territory without opposition, or (...) will an equilibrium of some small number of strategies emerge? Here it is shown, for finite configurations of Prisoner's Dilemma strategies embedded in a given infinite background, that such questions are formally undecidable: there is no algorithm or effective procedure which, given a specification of a finite configuration, will in all cases tell us whether that configuration will or will not result in progressive conquest by a single strategy when embedded in the given field. The proof introduces undecidability into decision theory in three steps: by (1) outlining a class of abstract machines with familiar undecidability results, by (2) modelling these machines within a particular family of cellular automata, carrying over undecidability results for these, and finally by (3) showing that spatial configurations of Prisoner's Dilemma strategies will take the form of such cellular automata. (shrink)

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible to explain (...) cooperation in the one-shot Prisoner's Dilemma in a way that is in accordance with some recent experimental findings. (shrink)

I first argue against Peter Singer's exciting thesis that the Prisoner's Dilemma explains why there could be an evolutionary advantage in making reciprocal exchanges that are ultimately motivated by genuine altruism over making such exchanges on the basis of enlightened long-term self-interest. I then show that an alternative to Singer's thesis — one that is also meant to corroborate the view that natural selection favors genuine altruism, recently defended by Gregory Kavka, fails as well. Finally, I show that even granting (...) Singer's and Kavka's claim about the selective advantage of altruism proper, it is doubtful whether that type of claim can be used in a particular sort of sociobiological argument against psychological egoism. (shrink)

In "Morals by Agreement," David Gauthier (1986) argues that it is rational to intend to cooperate, even in single-play Prisoner's Dilemma games, provided (1) your co-player has a similar intention; (2) both intentions can be revealed to the other player. To this thesis four objections are made. (a) In a strategic decision the parameters on which the argument relies cannot be supposed to be given. (b) Of each pair of a-symmetric intentions at least one is not rational. But it is (...) impossible to form symmetric intentions to cooperate conditionally. For the condition on which the decision depends cannot be fulfilled without deciding. (c) If one's intention has to be ascertained on the basis of information about one's past performance, it is straightforwardly rational to intend to cooperate, but there is no reason to do so in a single-play PD. (d) The argument cannot be extended to n-person games which are Gauthier's principal concern. (shrink)

Teaching economics has been shown to encourage students to defect in a prisoner's dilemma game. However, can ethics training reverse that effect and promote cooperation? We conducted an experiment to answer this question. We found that students who had the ethics module had higher rates of cooperation than students without the ethics module, even after controlling for communication and other factors expected to affect cooperation. We conclude that the teaching of ethics can mitigate the possible adverse incentives of the prisoner's (...) dilemma, and, by implication, the adverse effects of economics and business training. (shrink)

Experiments in which subjects play simultaneously several finite two-person prisoner's dilemma supergames with and without an outside option reveal that: (i) an attractive outside option enhances cooperation in the prisoner's dilemma game, (ii) if the payoff for mutual defection is negative, subjects' tendency to avoid losses leads them to cooperate; while this tendency makes them stick to mutual defection if its payoff is positive, (iii) subjects use probabilistic start and endeffect behavior.

Many recent studies of norm emergence employ the "prisoner's dilemma" (PD) paradigm, which focuses on the free-rider problem that can block the cooperation required for the emergence of social norms. This paper proposes an expansion of the PD paradigm to include a closely related game termed the "altruist's dilemma" (AD). Whereas egoistic behavior in the PD leads to collectively irrational outcomes, the opposite is the case in the AD: altruistic behavior (e.g., following the Golden Rule) leads to collectively irrational outcomes, (...) whereas egoistic behavior leads to Pareto-optimal outcomes. The analysis shows that PDs can be converted into ADs either by increasing cooperation costs or by diminishing marginal gains from cooperation; therefore ADs are as empirically abundant as PDs. In addition, the analysis shows that altruists are not the only type of actors who fall prey to the AD; egoists can fall into this trap as well if they possess a capacity for interpersonal control. Where group solidarity is defined analytically in terms of the extent of cooperation in both PDs and ADs, this paper presents a model based on rational choice to account for variations in solidarity. According to the proposed analysis, levels of group solidarity depend on the balance in the group between compliant control, which increases cooperation, and oppositional control, which reduces it. That balance, in turn, depends on the allocation of power within the group. (shrink)

The results of a series of computer simulations demonstrate how the introduction of separate spatial dimensions for agent interaction and learning respectively affects the possibility of cooperation evolving in the repeated prisoner's dilemma played by populations of boundedly-rational agents. In particular, the localisation of learning promotes the emergence of cooperative behaviour, while the localisation of interaction has an ambiguous effect on it.

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)

According to the so-called “Folk Theorem” for repeated games, stable cooperative relations can be sustained in a Prisoner’s Dilemma if the game is repeated an indefinite number of times. This result depends on the possibility of applying strategies that are based on reciprocity, i.e., strategies that reward cooperation with subsequent cooperation and punish defectionwith subsequent defection. If future interactions are sufficiently important, i.e., if the discount rate is relatively small, each agent may be motivated to cooperate by fear of retaliation (...) in the future. For finite games, however, where the number of plays is known beforehand, there is a backward induction argument showing that rational agents will not be able to achieve cooperation. On behalf of the Hobbesian “Foole”, who cannot see any advantage in cooperation, Gregory Kavka (1983, 1986) has presented an argument that significantly extends the range of the backward induction argument. He shows that, for the backward induction argument to be effective, it is not necessary that the precise number of future interactions be known. It is sufficient that there is a known definite upper bound on the number of interactions. A similar argument is developed by John W. Carroll (1987). We will here question the assumption of a known upper bound. When the assumption is made precise in the way needed for the argument to go through, its apparent plausibility evaporates. We then offer a reformulation of the argument, based on weaker, and more plausible, assumptions. (shrink)

Rachlin basically marshals three reasons behind his unconventional claim that altruism is a subcategory of self-control and that, hence, the prisoner's dilemma is the appropriate metaphor of altruism. I do not find any of the three reasons convincing. Therefore, the prisoner's dilemma metaphor is unsuitable for explaining altruism.

Donald Green and Ian Shapiro argue that rational choice scholarship in political science is excessively theory?driven: too few of its theoretical insights have been subjected to serious empirical scrutiny and survived. But rational choice theorizing has the potential to identify and correct logical inconsistencies and slippages. It is thus valuable even if the resulting theories are not tested empirically. When Green and Shapiro's argument concerning collective dilemmas and free riding is formalized, it turns out to be deeply flawed and in (...) many respects outright false. Their mistake is common enough: they misclassify a variety of collective dilemmas as prisoner's dilemmas. Because they misunderstand the theory of rational choice, Green and Shapiro allege that it is refuted by empirical findings that, in fact, support it. (shrink)

For the tradition, an action is rational if maximizing; for Gauthier, if expressive of a disposition it maximized to adopt; for me, if maximizing on rational preferences, ones whose possession maximizes given one's prior preferences. Decision and Game Theory and their recommendations for choice need revamping to reflect this new standard for the rationality of preferences and choices. It would not be rational when facing a Prisoner's Dilemma to adopt or co-operate from Amartya Sen's "Assurance Game" or "Other Regarding" preferences. (...) But there are preferences which it maximizes to adopt and co-operate from. (shrink)

I distinguish and review six major attempts to give a Co-operative solution to the Prisoners Dilemma: Symmetry, Mechanism, Inducement, Resolution, Alternative Principle, and Preference-Revision. I then detail and criticize those of Ned McClennen (Resolution/possibly Preference-Revision)and David Gauthier (Alternative Principle). I conclude with some observations about what the failure of their solutions shows must be the parameters of any correct Co-operative solution: Rational agents should adopt maximizing dispositions, i.e., ones which will induce them to Co-operate with just those similarly disposed, but (...) adopting the dispositions must consist in adopting revised preferences, ones favoring Co-operating under certain conditions, and able to rationalize it as straightforwardly maximizing on the new preferences. Co-operation would then be rationalized by the new preferences. Still, we will not know exactly which preference-function PD agents should adopt, only that it must maximize to adopt it, and maximize to Co-operate from it with similar agents. The details are complicated, and must await further study. (shrink)

I argue that Gauthier's constrained-maximizer rationality is problematic. But standard Maximizing Rationality means one's preferences are only rational if it would not maximize on them to adopt new ones. In the Prisoner's Dilemma, it maximizes to adopt conditionally cooperative preferences. (These are detailed, with a view to avoiding problems of circularity of definition.) Morality then maximizes. I distinguish the roles played in rational choices and their bases by preferences, dispositions, moral and rational principles, the aim of rational action, and rational (...) decision rules. I argue that Maximizing Rationality necessarily structures conclusive reasons for action. Thus conations of any sort can base rational choices only if the conations are structured like a coherent preference function; rational actions maximize on such functions. Maximization-constraining dispositions cannot integrate into a coherent preference function. (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)

David Gauthier thinks agents facing a prisoner's dilemma ('pd') should find it rational to dispose themselves to co-operate with those inclined to reciprocate (i.e., to acquire a constrained maximizer--'cm'--disposition), and to co-operate with other 'cmers'. Richmond Campbell argues that since dominance reasoning shows it remains to the agent's advantage to defect, his co-operation is only rational if cm "determines" him to co-operate, forcing him not to cheat. I argue that if cm "forces" the agent to co-operate, he is not acting (...) at all, never mind rationally. Thus, neither author has shown that co-operation is rational action in a pd. (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.

– We present a new paradigm extending the Iterated Prisoner's Dilemma to multiple players. Our model is unique in granting players information about past interactions between all pairs of players – allowing for much more sophisticated social behaviour. We provide an overview of preliminary results and discuss the implications in terms of the evolutionary dynamics of strategies.

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)

This paper proposes a view uniformly extending expected utility calculations to both individual and group choice contexts. Three related cases illustrate the problems inherent in applying expected utility to group choices. However, these problems do not essentially depend upon the tact that more than one agent is involved. I devise a modified strategy allowing the application of expected utility calculations to these otherwise problematic cases. One case, however, apparently leads to contradiction. But recognizing the falsity of proposition (1) below allows (...) the resolution of the contradiction, and also allows my modified strategy to resolve otherwise paradoxical cases of group choice such as the Prisoners' Dilemma: -/- (1) lf an agent x knows options A and B are both available, and x knows that were he to do A he would be better off (in every respect) than were he to do B, then doing A is more rational for x than doing B. (shrink)

Mankind soon learn to make interested uses of every right and power which they possess, or may assume. The public money and public liberty...will soon be discovered to be sources of wealth and dominion to those who hold them; distinguished, too, by this tempting circumstance, that they are the instrument, as well as the object of acquisition. With money we will get men, said Caesar, and with men we will get money. Nor should our assembly be deluded by the integrity (...) of their own purposes, and conclude that these unlimited powers will never be abused, because themselves are not disposed to abuse them. They should look forward to a time, and that not a distant one, when a corruption in this, as in the country from which we derive our origin, will have seized the heads of government, and be spread by them through the body of the people; when they will purchase the voices of the people, and make them pay the price. (shrink)

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)

According to a familiar argument, iterated prisoner's dilemmas of known finite lengths resolve for ideally rational and well-informed players: They would defect in the last round, anticipate this in the next to last round and so defect in it, and so on. But would they anticipate defections even if they had been cooperating? Not necessarily, say recent critics. These critics "lose" the backward-induction paradox by imposing indicative interpretations on rationality and information conditions. To regain it I propose subjunctive interpretations. To (...) solve it I stress that implications for ordinary imperfect players are limited. (shrink)

I have maintained that some but not all prisoners' dilemmas are side-by-side Necomb problems. The present paper argues that, similarly, some but not all versions of Newcomb's Problem are prisoners' dilemmas in which Taking Two and Predicting Two make an equilibrium that is dispreferred by both the box-chooser and predictor to the outcome in which only one box is taken and this is predicted. I comment on what kinds of prisoner's dilemmas Newcomb's Problem can be, and on opportunities that results (...) reached may open for kinds of cooperative reasoning in versions of Newcomb's Problem. (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)

Axelrod (The evolution of cooperation, 1984) and others explain how cooperation can emerge in repeated 2-person prisoner’s dilemmas. But in public good games with anonymous contributions, we expect a breakdown of cooperation because direct reciprocity fails. However, if agents are situated in a social network determining which agents interact, and if they can influence the network, then cooperation can be a viable strategy. Social networks are modelled as graphs. Agents play public good games with their neighbours. After each game, they (...) can terminate connections to others, and new connections are created. Cooperative agents do well because they manage to cluster with cooperators and avoid defectors. Computer simulations demonstrate that group formation and exclusion are powerful mechanisms to promote cooperation in dilemma situations. This explains why social dilemmas can often be solved if agents can choose with whom they interact. (shrink)

The paper attempts to rationalize cooperation in the one-shot prisoners' dilemma (PD). It starts by introducing (and preliminarily investigating) a new kind of equilibrium (differing from Aumann's correlated equilibria) according to which the players' actions may be correlated (sect. 2). In PD the Pareto-optimal among these equilibria is joint cooperation. Since these equilibria seem to contradict causal preconceptions, the paper continues with a standard analysis of the causal structure of decision situations (sect. 3). The analysis then raises to a reflexive (...) point of view according to which the agent integrates his own present and future decision situations into the causal picture of his situation (sect. 4). This reflexive structure is first applied to the toxin puzzle and then to Newcomb's problem, showing a way to rationalize drinking the toxin and taking only one box with-out assuming causal mystery (sect. 5). The latter result is finally extended to a rationalization of cooperation in PD (sect. 6). (shrink)

The paper is essentially a short version Spohn "Strategic Rationality" which emphasizes in particular how the ideas developed there may be used to shed new light on the iterated prisoner's dilemma (and on iterated Newcomb's problem).

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)

The Prisoner's Dilemma (PD) exhibits a tragedy in this sense: if the players are fully informed and rational, they are condemned to a jointly dispreferred outcome. In this essay I address the following question: What feature of the PD's payoff structure is necessary and sufficient to produce the tragedy? In answering it I use the notion of a trembling-hand equilibrium. In the final section I discuss an implication of my argument, an implication which bears on the persistence of the problem (...) posed by the PD. (shrink)

The purpose of this research is to examine the impact of individual and firm moral philosophies on marketing exchange relationships. Personal moral philosophies range from the extreme forms of true altruists and true egoists, along with three hybrids that represent middle ground (i.e., realistic altruists, tit-for-tats, and realistic egoists). Organizational postures are defined as Ethical Paradigm, Unethical Paradigm, and Neutral Paradigm, which result in changes to personal moral philosophies and company and industry performance. The study context is a simulation of (...) an exchange environment using a variation of the prisoners' dilemma game. A literature review is provided in the opening section, followed by details on the simulation, discussion of the results, and the implications for theory and practice. (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)