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.
Evolutionary applications of game theory present one of the most pedagogically accessible varieties of genuine, contemporary theoretical biology. We present here Oyun (OY-oon, http://charlespence.net/oyun), a program designed to run iterated prisoner’s dilemma tournaments, competitions between prisoner’s dilemma strategies developed by the students themselves. Using this software, students are able to readily design and tweak their own strategies, and to see how they fare both in round-robin tournaments and in “evolutionary” tournaments, where the scores in a given “generation” directly (...) determine contribution to the population in the next generation. Oyun is freely available, runs on Windows, Mac, and Linux computers, and the process of creating new prisoner’s dilemma strategies is both easy to teach and easy for students to grasp. We illustrate with two interesting examples taken from actual use of Oyun in the classroom. (shrink)
I first argue against Peter Singer's exciting thesis that the Prisoner'sDilemma 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 the spatialized Prisoner'sDilemma, 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'sDilemma 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'sDilemma strategies will take the form of such cellular automata. (shrink)
Experiments in which subjects play simultaneously several finite two-person prisoner'sdilemma supergames with and without an outside option reveal that: (i) an attractive outside option enhances cooperation in the prisoner'sdilemma 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.
We study the finitely repeated prisoner’s dilemma in which the players are restricted to choosing strategies which are implementable by a machine with a bound on its complexity. One player has to use a finite automaton while the other player has to use a finite perceptron. Some examples illustrate that the sets of strategies which are induced by these two types of machines are different and not ordered by set inclusion. Repeated game payoffs are evaluated according to the limit (...) of means. The main result establishes that a cooperation at almost all stages of the game is an equilibrium outcome if the complexity of the machines the players may use is limited enough and if the length T of the repeated game is sufficiently large. This result persists when more than T states are allowed in the player’s automaton. We further consider a variant of the model in which the two players are restricted to choosing strategies which are implementable by perceptrons and prove that the players can cooperate at most of the stages provided that the complexity of their perceptrons is sufficiently reduced. (shrink)
In the game theory literature, Garrett Hardin’s famous allegory of the “tragedy of the commons” has been modeled as a variant of the Prisoner’s Dilemma, labeled the Herder Problem (or, sometimes, the Commons Dilemma). This brief paper argues that important differences in the institutional structures of the standard Prisoner’s Dilemma and Herder Problem render the two games different in kind. Specifically, institutional impediments to communication and cooperation that ensure a dominant strategy of defection in the classic Prisoner’s (...)Dilemma are absent in the Herder Problem. Their absence does not ensure that players will achieve a welfare-enhancing, cooperative solution to the Herders Problem, but does create far more opportunity for players to alter the expected payoffs through cooperative arrangements. In a properly modeled Herder Problem—along the lines of an assurance game—defection would not always be the dominant strategy. Consequently, the Herder Problem is not in the nature of a Prisoner’s Dilemma. (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'sdilemma 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.
Conflict of interest may be modeled, heuristically, by the iterated Prisoner'sDilemma game. Although several researchers have shown that the Tit-For-Tat strategy can encourage the evolution of cooperation, this strategy can never outscore any opponent and it does poorly against its clone in a noisy environment. Here we examine the family of Pavlovian strategies which adapts its play by positive and negative conditioning, much as many animals do. Mutual cooperation will evolve in a contest with Pavlov against a (...) wide variety of opponents and in particular against its clone. And the strategy is quite stable in a noisy environment. Although this strategy cooperates and retaliates, as does Tit-For-Tat, it is not forgiving; Pavlov will exploit altruistic strategies until he is punished by mutual defection. Moreover, Pavlovian strategies are natural models for many real life conflict-of-interest encounters as well as human and computer simulations. (shrink)
Our Pavlov learns by conditioned response, through rewards and punishments, to cooperate or defect. We analyze the behavior of an extended play Prisoner'sDilemma with Pavlov against various opponents and compute the time and cost to train Pavlov to cooperate. Among our results is that Pavlov and his clone would learn to cooperate more rapidly than if Pavlov played against the Tit for Tat strategy. This fact has implications for the evolution of cooperation.
This paper clarifies some basic concepts or assumptions of the prisoner'sdilemma, asserts the independence between the two agentsA andB, and advocates the application of the dominance principle of decision theory to the prisoner'sdilemma. It discusses several versions of the prisoner'sdilemma, including the one-shot and repeated cases of a noncooperative game from a purely egoistic point of view. The main part of this paper, however, is a study of the problem from a (...) moral point of view through a special decision-theoretic approach. Morality is taken into account by incorporating the utility of the feeling of moral satisfaction for the agent, as a part of the total utility for the agent, into the decision-theoretic model. In this way the problem will appear as a purely technical decision problem, and the conflicts between various assumptions, or the dilemma caused by the problem, will no longer exist. It is also pointed out that in a more general case, for some values of the coefficient of moralityk, dominance will not exist so that the dominance principle will not be applicable. (shrink)
In a recent issue of this journal, C. L. Sheng claims to havesolved andexplained the Prisoner'sDilemma (PD) by studying it ‘from a moral point of view’ - i.e., by assuming that each player feels sympathy for the other. Sheng does not fully clarify this claim, but there is textual evidence that his point is this: PD's arise only for agents who feel little or no sympathy for each other; they cannot arise in the presence of a high (...) degree of reciprocal sympathy. A high degree of such sympathysolves the PD in that it prevents PD's from arising, and a low degree of itexplains the PD in that it provides an essential condition for the occurrence of that game. This thesis is false, as some examples show. These examples are important; they prevent us from underestimating the problem posed by the PD. (shrink)
In this paper a model of boundedly rational decision making in the Finitely Repeated Prisoner'sDilemma is proposed in which: (1) each player is Bayesianrational; (2) this is common knowledge; (3) players are constrained by limited state spaces (their Bayesian minds) in ‘processing’ (1) and (2). Under these circumstances, we show that cooperative behavior may arise as an individually optimal response, except for the latter part of the game. Indeed, such behaviorwill necessarily obtain in long enough games if (...) belief systems satisfy a natural condition: essentially, that all events consistent with the players' analysis of the game be attributed by them positive (although arbitrarily small) subjective probability. (shrink)
It is argued that, without a controversial and arguably mistaken assumption, Becker and Cudd's (1990) objections do not undermine the challenge raised by my (1987) model of iterated prisoner's dilemmas for the arguments of Taylor (1976, 1987) and others. Furthermore, it is argued that, even granting this assumption, there is an alternative model that avoids their objections.
This paper discusses the results of a single-shot Prisoner'sDilemma computer tournament. In the single-shot Prisoner'sDilemma tournament each pair of players interacts only once. But players can establish and detect reputations because they know how their current opponent has behaved in previous games with other players. The results show that cooperation is worthwhile, even in single-shot games, provided the outcomes of previous games are common knowledge.
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)
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)
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'sDilemma 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)
This article argues that various deviations from the basic principles of the scientific ethos – primarily the appearance of pseudoscience in scientific communities – can be formulated and explained using specific models of game theory, such as the prisoner’s dilemma and the iterated prisoner’s dilemma. The article indirectly tackles the deontology of scientific work as well, in which it is assumed that there is no room for moral skepticism, let alone moral anti-realism, in the ethics of scientific communities. (...) Namely, on the basis of the generally accepted dictum of scientific endeavor as the pursuit of knowledge exclusively for knowledge’s sake, scientifically »right« behavior is seen to be clearly defined and distinguishable from scientifically »wrong« behavior. After elucidating the basic principles of game theory, the article illustrates – by using imaginary and real cases, as well as some views from the philosophyof biology (the units of selection debate) – how this sort of reasoning could be applied in an analysis of the functioning of science. (shrink)
Teaching economics has been shown to encourage students to defect in a prisoner'sdilemma 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'sdilemma, and, by implication, the adverse effects of economics and business training. (shrink)
Rachlin basically marshals three reasons behind his unconventional claim that altruism is a subcategory of self-control and that, hence, the prisoner'sdilemma is the appropriate metaphor of altruism. I do not find any of the three reasons convincing. Therefore, the prisoner'sdilemma metaphor is unsuitable for explaining altruism.
Many recent studies of norm emergence employ the "prisoner'sdilemma" (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 "Prisoner'sDilemma" 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'sDilemma 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)
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)
The Prisoner'sDilemma (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)
According to David Lewis, the prisoner'sdilemma (PD) and Newcomb's problem (NP) are really just one dilemma in two different forms (Lewis 1979). Lewis's argument for this conclusion is ingenious and has been widely accepted. However, it is flawed. As this paper shows, the considerations that Lewis brings to bear to show that the game he starts with is an NP equally show that the game is not a PD.
A version of this paper was presented at the IEEE International Conference on Computational Intelligence, combined meeting of ICNN, FUZZ-IEEE, and ICEC, Orlando, June-July, 1994, and an earlier form of the result is to appear as "The Undecidability of the Spatialized Prisoner'sDilemma" in Theory and Decision . An interactive form of the paper, in which figures are called up as evolving arrays of cellular automata, is available on DOS disk as Research Report #94-04i . An expanded version (...) appears as chapter 6 of The Philosophical Computer. (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'sdilemma (and on iterated Newcomb's problem).
Hamilton games-theoretic conflict model, which applies Maynard Smith's concept of evolutionarily stable strategy to the Prisoner'sDilemma, 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'sDilemma.
– We present a new paradigm extending the Iterated Prisoner'sDilemma 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.
Several philosophers have discussed informal versions of a "symmetry argument" that seems to show that two rational maximizers will cooperate when they are in a prisoner'sdilemma. I present a more precise version of that argument and I argue that it is valid only if some crucial statements are misinterpreted as material conditionals instead of being interpreted correctly as subjunctive conditionals.
Revisiting Lacan's discussion of the puzzle of the prisoner'sdilemma provides a means of elaborating a theory of the trans-subjective. An illustration of this dilemma provides the basis for two important arguments. Firstly, that we need to grasp a logical succession of modes of subjectivity: from subjectivity to inter-subjectivity, and from inter-subjectivity to a form of trans-subjective social logic. The trans-subjective, thus conceptualized, enables forms of social objectivity that transcend the level of (inter)subjectivity, and which play a (...) crucial role in consolidating given societal groupings. The paper advances, secondly, that various declarative and symbolic activities are important non-psychological bases—trans-subjective foundations—for psychological identifications of an inter-subjective sort. These assertions link interesting to recent developments in the contemporary social psychology of interobjectivity, which likewise emphasize a type of objectivity that plays an indispensible part in co-ordinating human relations and understanding. (shrink)
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)
The repeated prisoner'sdilemma game is converted into a differential game by assuming that the players, instead of making decisions individually for each repetition of the prisoner'sdilemma game, make decisions on the ratio of cooperative and noncooperative games that they wish to play over the next few moves, and that the actual plays are then determined using this ratio and a randomizing procedure. Although it sounds like a significant departure, this assumption is probably not too (...) different from reality.Since each player can always obtain by his own action at least the payoff which he would receive from the noncooperative-noncooperative pair of strategies, that part of the differential game which is dominated by such a dual noncooperative strategy for either player is an unlikely outcome. This dominated area can be readily computed for any game, including those with more than two players.Formal testing with empirical data was impossible because of uncertainty about the proper null hypothesis. Nevertheless, experimental results reported by Rapoport are consistent with the theory. (shrink)
In conclusion, I shall indicate one consequence of (3.4). The major resultof work on infinitely iterated Prisoner'sDilemma games is that there existcooperative equilibria in such games. I have suggested above that myaccount of finitely, but indefinitely, iterated Prisoner'sDilemma gamesreflects the nature of genuine iterated Prisoner's Dilemmas more accu-rately than accounts involving infinite iterations. If my suggestion iscorrect, then one consequence of (3.4) - of there being only uncooperativeequilibria in finitely, but indefinitely, iterated games (...) - is to call intoquestion the significance of the existence of cooperative equilibria ininfinitely iterated Prisoner'sDilemma games. (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)
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'sdilemma, 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)