Prisoner's Dilemma

by

Marek M. Kaminski

• LAST REVIEWED: 30 June 2014
• LAST MODIFIED: 30 June 2014
• DOI: 10.1093/obo/9780199828340-0155

Introduction

The Prisoner’s Dilemma (PD) is a noncooperative 2x2 game (two players with two strategies each) that represents an apparently paradoxical phenomenon of independently rational decisions leading to socially suboptimal outcomes. In a popular interpretation, two robbers, who were caught by police and are held incommunicado, expect to be charged. They care only about their own sentences; they can stay mute or testify against their partner. The prosecutor describes to them the consequences of their decisions: if they both stay mute, there is not enough evidence for a serious charge and they will be charged with a minor crime. Their sentence will be one year in prison. If one inmate testifies, the other one will be convicted entirely on the strength of this testimony and given a three-year sentence. The testifying inmate will go free. If they both testify, such testimonies are relatively less valuable and they will each receive a two-year sentence. The dilemma is constituted by two facts. First, testifying is a dominant strategy; that is, it is always better than staying mute. If one inmate stays mute, then the other one goes free for testifying versus one year in jail for staying mute; if one inmate testifies, then the other one gets two years for testifying and three years for staying mute. Second, when both inmates testify, they both get lower payoffs (longer sentences) than when they stay mute: two years versus only one year. Thus, in the Prisoner’s Dilemma, individual rationality leads to social suboptimality. Every 2x2 game such that both players have dominant strategies that lead to worse outcomes for both players than their dominated strategies is called a Prisoner’s Dilemma. The “dilemma” in PD results from the fact that players following gains impose external costs on opponents that turn out to be greater than that opponent’s own gain from the corresponding strategy. Numerous situations in economics, political science, psychology, and sociology, as well as biology and management science, have the structure of PD. The dilemma can be extended to its multiplayer and repeated versions. Examples of empirical situations modeled by PD include the overexploitation of natural resources, global warming, an arms race, or problems of collective action. For instance, two superpowers may have incentive to unilaterally upgrade their weapon systems at a large cost, and thus gain some edge over the opponent. When both do that, they are both worse off, since the balance of power is unchanged but substantial cost was paid for the upgrade. The rise of PD, along with game theory in general, has contributed to the unification of the social sciences and related fields. The author is grateful for comments to Barbara Kataneksza. The support of the Center for the Study of Democracy at the University of California, Irvine is gratefully acknowledged.

General Overviews

Poundstone 1992 is a popular book with a wealth of anecdotes, historical material, and examples from game theory, with the main focus on the PD. Hardin 1982 provides a comprehensive and systematic overview of problems of collective action that Hardin defines as multiplayer PD. Hardin discusses psychological and philosophical aspects of collective action as well as institutional solutions and conventions. Sandler 1992 provides an economic analysis of collective action problems in a broader sense, explicitly going beyond multiplayer PD, and including some coordination problems and similar games. Sandler focuses on issues such as group size, composition, and asymmetries, as well as the technology of supply of goods. Both Hardin’s and Sandler’s books assume as a point of departure Olson 1965 (cited under Classical Applications) on the logic of collective action. The introduction to Roth and Kagel 1995 provides a review of experiments with PD, while Ledyard 1995 (Chapter 2 of the same volume) focuses on experimental research studying the factors facilitating cooperation in public goods provision. Komorita and Parks 1994 summarizes early work in psychological research on social dilemmas and relevant work in other disciplines. Ostrom 2000 provides an accessible introduction to all types of research on collective action.

• Hardin, Russell. 1982. Collective action. Baltimore: Johns Hopkins Univ. Press.

  Comprehensive overview of problems of collective action defined as multiplayer, PD and possible solutions.

• Komorita, Samuel S., and Craig D. Parks. 1994. Social dilemmas. Madison, WI: Brown & Benchmark.

  Summary of early work in psychological research on social dilemmas and relevant work in other disciplines.

• Ledyard, John O. 1995. Public goods: A survey of experimental research. In The handbook of experimental economics. Vol. 1. Edited by Alvin E. Roth and John Henry Kagel, 111–194. Princeton, NJ: Princeton Univ. Press.

  Discussion of various aspects of public goods provision and experimental research that studies factors facilitating cooperation.

• Ostrom, Elinor. 2000. Collective action and the evolution of social norms. Journal of Economic Perspectives 14.3: 137–158.

  DOI: 10.1257/jep.14.3.137

  Provides an accessible introduction to all types of research on collective action.

• Poundstone, William. 1992. Prisoner’s Dilemma. New York: Anchor Books.

  Historical overview of events and people behind the development of game theory and the PD. Informal discussion of social dilemmas, games related to the PD, and repeated PD, with a wealth of examples and anecdotes.

• Roth, Alvin E., and John Henry Kagel, eds. 1995. The handbook of experimental economics. Vol. 1. Princeton, NJ: Princeton Univ. Press.

  Detailed description of a number of experiments with substantial space devoted to PD, especially in Roth’s introduction and Ledyard’s chapter 2.

• Sandler, Todd. 1992. Collective action: Theory and applications. Ann Arbor: Univ. of Michigan Press.

  Economic analysis of collective action and theoretical developments since Olson’s founding contribution (Olson 1965, cited under Classical Applications). Discusses public goods, club goods, and their levels of excludability and rivalry.