Category Archives: Game Theory

Game theory, which uses mathematical models to study human behavior and interactions in games, has applications in areas that range widely from politics and economics to warfare and international relations. It has even been used in the study of conflict and cooperation.

One of the best known examples of game theory in action is the Prisoner’s Dilemma, a non-zero sum game used to analyze cooperation.

The basic premise of the Prisoner’s Dilemma is this: the police have arrested two individuals suspected of being co-conspirators in a crime. The police keep these individuals in separate cells to prevent them from communicating with each other. The police lack enough evidence to convict either of them but offer each of them a deal in the hopes that either or both of them will confess. They tell each prisoner that if he betrays his accomplice, he will go free. If both prisoners refuse to talk, they will both receive only a very light prison sentence because of the lack of evidence. If one betrays the other, the one who betrays will go free, and the one who says nothing will be punished with a lengthy prison sentence. If, however, they both betray each other, they will receive prison sentences, but not as lengthy as if only one confesses.

The dilemma of course is that neither prisoner can speak with the other, so neither knows which course of action the other will choose—will they remain silent, thereby cooperating with each other, or will one or both of them betray the other? The biggest payoff for one prisoner occurs if one betrays while the other remains silent; the best outcome for both prisoners occurs if they both remain silent, thereby drawing only a light sentence.

The choice lies between cooperation and competition. Does the prisoner think only of himself or take his fellow prisoner into account?

(Interesting aside: according to Wikipedia, there is actually a television game show, “Friend or Foe“, which utilizes the Prisoner’s Dilemma in dividing up winnings among members of the team that scores the lowest on the show.)

Of course in real-life conflicts or negotiations, people are able to do what the prisoners in the Prisoner’s Dilemma are unable to: talk to each other. Communication removes the risk and unpredictability that silence produces: without communication, an individual can only anticipate or guess what the person across the bargaining table will do. Communication with the disclosure it brings reveals interests and builds trust. Through communication it is possible to address or minimize risk, discuss contingencies, design mutually beneficial outcomes, and optimize proposals already on the table to maximize benefit. This provides significant rewards for cooperative behavior.

The Prisoner’s Dilemma can be played online at several web sites. These include:

• The Serendip web site, a “gathering place for people who suspect that life’s instructions are always ambiguous and incomplete” (you can’t argue with that).
• Iterated-prisoners-dilemma.net, which allows you to change players’ strategies and run simulations using a number of different variables.
• Prisoners-dilemma.com, where you can also play the game against the computer using different strategies. Click on the link for http://www.princeton.edu/~mdaniels/PD/PD.html to play the game.