When does self-interest counsel cooperation? This question pertains both to the labile behaviors produced by rational deliberation and to the more instinctive and fixed behaviors produced by natural selection. In both cases, a standard starting point for the investigation is the one-shot prisoners' dilemma. In this game, each player has the option of producing one or the other of two behaviors. The pay-offs to the row player are as follows.

Maximizers in isolated Prisoner's Dilemmas are doomed to frustration. But in Braybrooke's view maximizers might do better in a series, securing Pareto-optimal arrangements if not from the very beginning, at least eventually. Given certain favourable special conditions, it can be shown according to Braybrooke and shown even without question-begging motivational or value assumptions, that in a series of Dilemmas maximizers could manage to communicate a readiness to reciprocate, generate thereby expectations of reciprocation, and so give rise to optimizing reciprocations (...) which, in due course, would reinforce expectations, the net result of all this being an increasingly stable practice to mutual benefit. In this way neighbours could learn to be good neighbours: they could learn to respect each other's property, to engage in reciprocal assistance, and perhaps even to make and keep promises covering a range of activities. So maximizers are, Braybrooke holds, capable of a society of sorts. Out of the ashes they might build something. But even under favourable conditions they could not build much and most conditions would defeat them almost entirely, for many-person Dilemmas whether isolated or in series would be quite beyond them, question-begging motivational assumptions aside. In settings at all like those in which we live, utility maximization assuming only ‘traditional’ motivation is self-defeating without remedy, and most certainly not an adequate basis for social life.' The probable inference from as a conception of individual rationality: for surely truly rational agents would be if not perfectly well designed at least better designed for communal living than utility maximizers would be assuming only ‘traditional’, non-question-begging values or motivation. Or, if this inference is denied and maximization is not challenged as a conception of rationality, we can conclude instead, Braybrooke has more recently suggested, that the advice, ‘Be rational,’ is incomplete, and when addressed to groups should be supplemented by, ‘And be somewhat ‘untraditional’ in your values; respect at least some rules that would make coordination and cooperation possible even in many-person interaction problems.’. (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)

There are two curious features about the backward induction argument (BIA) to the effect that repeated non-cooperation is the rational solution to the finite iterated prisoner’s dilemma (FIPD). First, however compelling the argument may seem, one remains hesitant either to recommend this solu- tion to players who are about to engage in cooperation or to explain cooperation as a deviation from rational play in real-life FIPD’s. Second, there seems to be a similarity between the BIA for the (...) FIPD and the surprise exam paradox (SEP) and one cannot help but wonder whether the former is indeed no more than an instance of the latter. I argue that there is an important difference between the BIA for the FIPD and the SEP, but that a comparison to the SEP can help us understand why the conclusion of the BIA for the FIPD strikes us as a counterintuitive solution to real-life FIPD’s. (shrink)

Several recent commentators have suggested that for fully rational agents who find themselves in iterated prisoner's dilemmas of indefinite length, co-operation is the rational strategy. Their argument is that these fully rational agents can be taught, through the co-operative actions of other agents, to bypass the dominant move of noncooperation and co-operate instead. The proponents of the “teaching strategy” seem to have ignored the compelling argument of Jordan Howard Sobel. While the teaching argument may work for agents who (...) are less than purely rational, Sobel has pointed out that hyperrational utility maximizers cannot be taught; they reason deductively, not inductively, as the “teaching argument” requires. (shrink)

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)

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).

– 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.

David Lewis has argued that we can gain helpful insight to the Prisoners' Dilemmas that we face from the fact that Newcomb's Problems are easy to solve, and the fact that Prisoners' Dilemmas are nothing other than two Newcomb Problems side by side. The present paper shows that the Prisoners' Dilemmas that we face are significantly different from Newcomb Problems in that the former are iterated while the latter are not. Thus Lewis's hope that we can get insight into (...) the former from the latter is illusory. (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)

I present a game-theoretic way to understand the situation describing Newcomb’s Problem (NP) which helps to explain the intuition of both one-boxers and two-boxers. David Lewis has shown that the NP may be modelled as a Prisoners Dilemma game (PD) in which ‘cooperating’ corresponds to ‘taking one box’. Adopting relevant results from game theory, this means that one should take just one box if the NP is repeated an indefinite number of times, but both boxes if it is a (...) one-shot game. Causal decision theorists thus give the right answer for the one-shot situation, whereas the one-boxers’ solution applies to the indefinitely iterated case. Because Nozick’s set-up of the NP is ambiguous between a one-shot and a repeated game, both of these solutions may appear plausible – depending on whether one conceives of the situation as one-off or repeated. If the players’ aim is to maximize their payoffs, the symmetric structure of the PD implies that the two players will behave alike both when the game is one-shot and when it is played repeatedly. Therefore neither the observed outcome of both players selecting the same strategy (in the PD) nor, correspondingly, the predictor’s accurate prediction of this outcome (in the NP) is at all surprising. There is no need for a supernatural predictor to explain the NP phenomena. (shrink)

The iterated Prisoner’s Dilemma has become the standard model for the evolution of cooperative behavior within a community of egoistic agents, frequently cited for implications in both sociology and biology. Due primarily to the work of Axelrod (1980a, 198Ob, 1984, 1985), a strategy of tit for tat (TFT) has established a reputation as being particularly robust. Nowak and Sigmund (1992) have shown, however, that in a world of stochastic error or imperfect communication, it is not TFT that (...) finally triumphs in an ecological model based on population percentages (Axelrod and Hamilton 1981), but ‘generous tit for tat’ (GTFT), which repays cooperation with a probability of cooperation approaching 1 but forgives defection with a probability of l/3. In this paper, we consider a spatialized instantiation of the stochastic Prisoner’s Dilemma, using two-dimensional cellular automata (Wolfram, 1984, 1986; Gutowitz, 1990) to model the spatial dynamics of populations of competing strategies. The surprising result is that in the spatial model it is not GIFT but still more generous strategies that are favored. The optimal strategy within this spatial ecology appears to be a form of ‘bending over backwards’, which returns cooperation for defection with a probability of 2/3 - a rate twice as generous as GTFT. (shrink)

Setting aside various foundational moral entanglements, I will offer an argument for the protection of intellectual property based on individual self-interest and prudence. In large part, this argument will parallel considerations that arise in a prisoner’s dilemma game. After sketching the salient features of a prisoner’s dilemma, I will briefly examine the nature of intellectual property and how one can view content creation, exclusion, and access as a prisoner’s dilemma. In brief, allowing content to (...) be unprotected in terms of free access leads to a sub-optimal outcome where creation and innovation are suppressed. Finally, I will argue that adopting the institutions of copyright, patent, and trade secret is one way we can avoid these sub-optimal results. (shrink)

The study explores the impact of robots’ emotional displays on people’s tendency to cooperate with a robot opponent in prisoner’s dilemma games. Participants played iterated prisoner’s dilemma games with a non-expressive robot (as a measure of cooperative baseline), followed by an angry, and a sad robot, in turn. Based on the Emotion as Social Information model, we expected participants with higher cooperative predispositions to cooperate less when a robot displayed anger, and cooperate more when the (...) robot displayed sadness. Contrarily, according to this model, participants with lower cooperative predispositions should cooperate more with an angry robot and less with a sad robot. The results of 60 participants failed to support the predictions. Only the participants’ cooperative predispositions significantly predicted their cooperative tendencies during gameplay. Participants who cooperated more in the baseline measure also cooperated more with the robots displaying sadness and anger. In exploratory analyses, we found that participants who accurately recognised the robots’ sad and angry displays tended to cooperate less with them overall. The study highlights the impact of personal factors in human–robot cooperation, and how these factors might surpass the influence of bottom-up emotional displays by the robots in the present experimental scenario. (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)

In this paper we compare two micro foundations for modelling human behaviour and decision making. We focus on perfect strategic rationality on the one hand and a simple reinforcement mechanism on the other hand. Iterated prisoner’s dilemmas serve as the play ground for the comparison. The main lesson of our analysis is that in the space of all possible 2 × 2 PDs different micro foundations do matter. This suggests that researchers can not safely rely on the assumption (...) that implementing simple models of decision making will yield the same results that may be obtained when more sophisticated decision rules are built into the agents. (shrink)

For over a decade neuroscience has uncovered that appropriate decision-making in daily life decisions results from a strong interplay between cognition and covert biases produced by emotional processes. This interplay is particularly important in social contexts: lesions in the pathways supporting these processes provoke serious impairments on social behavior. One important mechanism in social contexts is empathy, fundamental for appropriate social behavior. This paper presents arguments supporting this connection between cognition and emotion, in individual as well as in social contexts. (...) The central claim of this paper is that biologically inspired cognitive architectures ought to include these mechanisms. A taxonomy of computational models addressing emotions is presented, together with a brief survey of the research published in this area. The Prisoner Dilemma game is used as a case study exposing the trade-off between individual rationality and cooperative behavior. Experiments using a simple implementation of empathy and emotion expression, employing an Iterated Prisoner Dilemma setup, illustrate the emergence of a cooperative behavior mutually beneficial for both players. (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 modelsof 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 – how this sort of reasoning could be applied in an analysis of the functioning of science.U članku se tvrdi da se različite devijacije od osnovnih načela etosa znanosti – prije svega pojava pseudoznanosti u znanstvenim zajednicama – mogu formulirati i objasniti pomoću specifičnih modela teorije igara kao što su zatvorenikova dilema i ponovljena zatvorenikova dilema. Članak se, prema tome, neizravno bavi i deontologijom znanstvenoga rada, pri čemu je ključna pretpostavka da u etici znanstvenih zajednica nema mjesta moralnom skepticizmu, a kamoli moralnom antirealizmu: naime, znanstveno »ispravno« ponašanje smatra se jasno definiranim i razlučivim od znanstveno »pogrešnog« ponašanja na osnovi općeprihvaćene maksime znanstvenoga rada kao potrage za znanjem isključivo radi znanja. Nakon izlaganja osnovnih načela teorije igara, pokazuje se – koristeći se imaginarnim i zbiljskim slučajevima, kao i nekim stavovima iz filozofije biologije – kako bi se ovu vrstu razmišljanja moglo primijeniti u analizi funkcioniranja znanosti. (shrink)

Ainslie challenges our interpretation of the properties of hyperbolic discount curves in an iterated prisoners’ dilemma model. In this reply, we discuss the emergence of hyperbolic discount functions in the behavioral economics literature and evaluate their properties. Furthermore, we present a summarized version of our IPD model and evaluate Ainslie’s points of contention.

Louis Marinoff [1990] criticizes Axelrod and Hamilton's [1981] use of the concept of an evolutionarily stable strategy, and claims to find an inconsistency between their theory for repeated Prisoner's Dilemma games and empirical results. Marinoff seeks to resolve the inconsistency by arguing that Axelrod and Hamilton's model is ill conceived: he purports to prove, contra Axelrod and Hamilton, that no evolutionarily stable strategy exists in the repeated Prisoner's Dilemma. But his argument is flawed, and moreover, Marinoff (...) gives no good reason for thinking the claimed discrepancy between thory and empirical results exists. (shrink)

This case raises the difficult question of how to respond to patients who appear to lack decision-making capacity, yet retain limited communication that allows them to state a preference for life-sustaining treatment that conflicts with the choice of their surrogate. I argue that the patient’s preference should be honored, even though the patient lacks decision-making capacity, and the preference contradicts the wishes of the surrogate.

Among various cases that equally admit of evidentialist reasoning, the supposedly evidentialist solution has varying degrees of intuitive attractiveness. I suggest that cooperative reasoning may account for the appeal of apparently evidentialist behavior in the cases in which it is intuitively attractive, while the inapplicability of cooperative reasoning may account for the unattractiveness of evidentialist behaviour in other cases. A collective causal power with respect to agreed outcomes, not evidentialist reasoning, makes cooperation attractive in the Prisoners' Dilemma. And a (...) natural though unwarranted assumption of such a power may account for the intuitive appeal of the one-box response in Newcomb's Problem. (shrink)

In this paper, I discuss the problems of ``order in social situations'' using a computer simulation of iterated N -person prisoners' dilemma game. It has been claimed that, in the case of the 2 -person prisoners' dilemma, repetition of games and the reciprocal use of the ``tit-for-tat'' strategy promote the possibility of cooperation. However, in cases of N -person prisoners' dilemma where N is greater than 2, the logic does not work effectively. The most essential problem (...) is so called ``sanctioning problems''. In this paper, firstly, I discuss the ``sanctioning problems'' which were introduced by Axelrod and Keohane in 1986. Based on the model formalized by Axelrod, I propose a new model, in which I added a mechanism of players' payoff changes in the Axelrod's model. I call this mechanism norm-internalization and call our model `` norm-internalization game ''. Second, by using the model, I investigated the relationship between agents' norm-internalization (payoff-alternation) and the possibilities of cooperation. The results of computer simulation indicated that unequal distribution of cooperating norm and uniform distribution of sanctioning norm are more effective in establishing cooperation. I discuss the mathematical features and the implications of the results on social science. (shrink)

If social relations often require the choice of a cooperative solution to a prisoners' dilemma, we must ask how people generally solve the games. Three possible devices are that those who choose non-cooperative strategies get a bad reputation and so learn to be cooperative, that people are taught by parents that non-cooperators have unhappy lives, or that an official can be paid a salary to make the cooperative choice. By analyzing erotic love and marriage, and why people try to (...) do their jobs, it is suggested that these devices result in people often solving prisoners' dilemma games without being conscious of them. How then do these structures that 'have the function' of solving prisoners' dilemmas get created and maintain themselves? It is suggested that Deweyan consciousness, existing only when structural strains or unsolved games create personal problems, is adequate to explain many such functional structures. (shrink)

In this essay I shall try to show that the egoist's inability to avoid the Prisoners’ Dilemma is not a reason for rejecting egoism. In the first section I shall outline the Prisoners’ Dilemma and indicate why the egoist cannot avoid the dilemma. In the next section I shall consider an argument against egoism based upon an appeal to our intuitions as to what is rational. And in the final section I shall consider the argument that egoism (...) is not self-supporting and so is not an adequate conception of rationality.But first a few words should be said about what is meant by egoism here. The egoist is commonly thought of as someone who acts from selfinterest. This is in keeping with the present use of the term as long as ‘self-interest’ is not understood in a too narrow a fashion. Perhaps a Jess misleading way of characterizing the egoist, though, is as someone who tries to maximize his happiness - i.e., he is an individual utility maximizer. (shrink)

Simon Blackburn has claimed that on a theory of revealed preference it is tautological that any eligible player - one whose preferences are consistent - plays hawk, chooses a strategy of non-cooperation with the other prisoner. This claim is examined and rejected. A prisoner in the appropriate sense is defined not by preferences over actions (playing hawk or playing dove) but by preferences over the four possible outcomes which result from the players' actions jointly (both playing hawk, both (...) playing dove, the first playing hawk and the second dove, and vice versa). It is not inconsistent to suppose that a prisoner has the appropriate preferences over outcomes but nevertheless chooses to play dove. This can happen either if the prisoner believes for some reason that the full range of outcomes is not available, or if the prisoner is simply a bad strategic thinker. It is perhaps tautological that a player with the appropriate preferences over outcome and with suitable beliefs will if rational choose to play hawk. However, rationality would then involve an appeal to a further principle, the sure-thing principle: if a prisoner would choose hawk knowing that the other will choose hawk, and would also choose hawk knowing that the other will choose dove, then hawk should be chosen when it is uncertain what the other will choose. (shrink)

We make the case that the Prisoner’s Dilemma, notwithstanding its fame and the quantity of intellectual resources devoted to it, has largely failed to explain any phenomena of social scientific or biological interest. In the heart of the paper we examine in detail a famous purported example of Prisoner’s Dilemma empirical success, namely Axelrod’s analysis of WWI trench warfare, and argue that this success is greatly overstated. Further, we explain why this negative verdict is likely true (...) generally and not just in our case study. We also address some possible defenses of the Prisoner’s Dilemma. (shrink)

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)

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)