Prisoner's Dilemma

This paper presents a problem for a prisoner’s dilemma model according to which the state of nature would be a war of all against all, which I call “the close up problem.”.

Game theory involves deliberating about what to do in light of what other people are likely to do. One of the central frameworks of game theory is the prisoner’s dilemma, in which participants who make rational choices end up in suboptimal outcomes. Using the prisoner’s dilemma to model competition between firms sets the stage for a new and promising approach to business ethics: the market failures approach.

This article examines the prisoner's dilemma paradox and argues that confessing is the rational choice, despite this probably entailing a less-than-ideal outcome.

The lifting of lockdown is a typical case of the tragedy of the commons, and as such should be regulated by public authority, instead of being left to the ethics and responsibility of single individuals. I would therefore argue that we should think about an intermediate phase between the lockdown and the opening of shops (which in the Italian case is the transition from the red zone to the orange zone): diversified access to commercial activities, on an hourly basis, for (...) different population groups. This can be achieved either by creating different opening hours for different commercial activities and offices, or by opening them all at the same time but introducing free entrance hours based on age groups of clients. Both solutions would imply an extension of business and office hours, contrary to what has happened in most countries, where an attempt has been made to shorten the days and in some cases, such as in Italy, a curfew has even been introduced at a certain time of the day (in Italy, at 10 pm). (shrink)

The chapter reviews recent theoretical and empirical developments concerning the theory of team reasoning in game theoretic interactions.

Universal social institutions, such as marriage, commons management and property, have emerged independently in radically different cultures. This requires explanation. As Boyer and Petersen point out ‘in a purely localist framework would have to constitute massively improbable coincidences’ . According to Boyer and Petersen, those institutions emerged naturally out of genetically wired behavioural dispositions, such as marriage out of mating strategies and borders out of territorial behaviour. While I agree with Boyer and Petersen that ‘unnatural’ institutions cannot thrive, this one-sided (...) explanation of universal social institutions in terms of genetic human nature is unsatisfactory. Drawing on the literature on multi-level selection and gene-culture coevolution, I argue that universal social institutions are first and foremost the products of cultural selection. They occupy fitness peaks in the landscape of cultural possibilities, much in the same way that biological adaptations occupy fitness peaks in the landscape of biological possibilities. To show this, I use game-theory. By modelling the domains of social interaction in which marriage, commons management, and property emerged as Prisoner’s dilemma situations, it becomes clear how an institutional framework allows the group to move to an interactive equilibrium with a larger payoff. Institutions do so by incentivising all parties to adopt a cooperative strategy. They are culturally selected ways of optimising genetically constrained domains of human social interaction. (shrink)

As these opening quotes acknowledge, the Prisoner’s Dilemma (PD) represents a core puzzle within the formal mathematics of game theory.3 Its rise in conspicuity is evident figure 2.1 above demonstrating a relatively steady rise in incidences of the phrase’s usage between 1960 to 1995, with a stable presence persisting into the twenty first century. This famous two-person “game,” with a stock narrative cast in terms of two prisoners who each independently must choose whether to remain silent or speak, each advancing (...) self-interest at the expense of the other and thereby achieving a mutually suboptimal outcome, mires any social interaction it is applied to into perplexity. The logic of this game proves the inverse of Adam Smith’s invisible hand: individuals acting on self interest will achieve a mutually suboptimal outcome. However, as this chapter illuminates, the assumptions underlying game theory drive this conclusion. (shrink)

The theme of this issue of the St. Gallen Business Review is "Harmony". For this reason, we would like to discuss whether two aspects of our life- world are in harmony, namely economic optimization and morality. What is the relation between them? According to a widely shared view, which is one aspect of the doctrine of "mainstream economics", the functioning of an economic system does not require moral behaviour on the part of the individual economic agent. In what follows, we (...) will try to convince you that this is false. If all economic agents – managers, employees, bankers, consumers and so on – were purely self-interested, as mainstream economics assumes, our economic practice would fail. There are various reasons for this. Here we will focus on one of them, namely the pivotal role of interpersonal communication. (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)

"Romanticism, when attains a fullness of complexity..there occurs of the supernatural unique". http://philpapers.org/profile/112741.

A survey of some game-theoretic accounts of the emergence and evolution of spontaneuous cooperation in social and public-good dilemmas.

This is the introductory essay to the Italian translation of Matt Ridley's "The origins of virtue", surveying the game-theoretic and evolutionary approaches to the emergence and evolution of cooperation and altruism.

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 focuses on Anthony de Jasay's "anarcho-liberalism" as based oon his game-theoretic approach to the problem of public goods provision.

In Book III, Part 2 of the Treatise, Hume presents a natural history of justice. Self-interest clearly plays a central role in his account; our ancestors invented justice conventions, he maintains, for the sake of reciprocal advantage. But this is not what makes his approach so novel and attractive. Hume recognizes that prudential considerations are not sufficient to explain how human beings – with our propensities towards temporal discounting and free-riding – could have established conventions for social exchange and collective (...) action in commercial societies. This leads him to develop an innovative account of the role that emotional aversions play in establishing trust between strategically rational agents. (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)

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)

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)

n 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 configurationns of Prisoner’s Dilemma strategies will take the form of such cellular automata. (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)

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)

David Gauthier argues that it can be rational to perform a non-maximizing cooperative act, since there are certain situations in which it is rational to adopt an intention to perform a non-maximizing cooperative act, and since if it is rational to adopt an intention to do something, then it is rational to do that thing. An important objection to this argument focuses on the move from the rationality of adopting intentions to the rationality of acting on them. Gregory Kavka argues (...) that there are other situations – involving deterrence rather than cooperation – in which it is rational to adopt an intention to perform an irrational retaliatory action, that these situations and the cooperative ones are relevantly similar, so that, in the original cooperative situations, it is rational to adopt an intention to cooperate but irrational actually to cooperate. In this paper, I examine one way in which the argument for cooperation may be reformulated to circumvent this particular objection. (shrink)

This paper reviews six attempts to give cooperative solutions to Prisoners Dilemmas: symmetry (agents are in identical situations, so should choose the same way, so should both choose cooperation because that’s better for each), mechanism (each agent should delegate the decision to a machine which will choose cooperation for them provided the other does likewise), inducement (the agents should make a side bet which pays off only upon both cooperating), resolution (each agent should resolve to cooperate, then act on the (...) resolution), alternative principle (rationality requires not dominance reasoning and so defecting, but constrained maximization or resolution compliance or “sophisticated” choosing, and so cooperation), and preference revision (each agent should acquire conditional preferences to cooperate, then cooperate provided the other agent has acquired similar preferences). It distinguishes one-stage from two-stage games, as well as endogenously available solutions (ones available to agents in the circumstances of the game merely due to the nature of rationality) from solutions requiring exogenous devices. It contrasts Edward McClennen’s endogenous solution, which is some combination of resolution and alternative principle solution, with David Gauthier’s endogenous alternative principle solution. It argues that all have problems, ones best solved by the endogenous preference revision solution defended by Duncan MacIntosh. (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 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)

"From the Proceedings of the British Academy, London, volume LXV (1979)" - title page. Series: Henrietta Hertz Trust annual philosophical lecture -- 1978 Other Titles: Proceedings of the British Academy. Vol.65: 1979.

The game theoretic notion of best-response reasoning is sometimes criticized when its application produces multiple solutions of games, some of which seem less compelling than others. The recent development of the theory of team reasoning addresses this by suggesting that interacting players in games may sometimes reason as members of a team – a group of individuals who act together in the attainment of some common goal. A number of properties have been suggested for team-reasoning decision-makers’ goals to satisfy, but (...) a few formal representations have been discussed. In this paper we suggest a possible representation of these goals based on the notion of mutual advantage. We propose a method for measuring extents of individual and mutual advantage to the interacting decision-makers, and define team interests as the attainment of outcomes associated with maximum mutual advantage in the games they play. (shrink)

This paper is intended as a critical examination of the question of when and under what conditions the use of computer simulations is beneficial to scientific explanations. This objective is pursued in two steps: First, I try to establish clear criteria that simulations must meet in order to be explanatory. Basically, a simulation has explanatory power only if it includes all causally relevant factors of a given empirical configuration and if the simulation delivers stable results within the measurement inaccuracies of (...) the input parameters. -/- In the second step, I examine a few examples of Axelrod-style simulations as they have been used to understand the evolution of cooperation (Axelrod, Schüßler). These simulations do not meet the criteria for explanatory validity and it can be shown, as I believe, that they lead us astray from the scientific problems they have been addressed to solve. (shrink)