Prisoner's Dilemma Glossary

PRISONER'S DILEMMA GLOSSARY

Cardinal Payoffs: The most common payoff structure for the prisoner's dilemma employs ordinal payoffs which simply rank the payoffs from best to worse. In contrast, cardinal payoffs involve assigning a value (dollars, utility, etc.) to each payoff. By using cardinal payoffs, intensity of the game can be varied by making the sucker's payoff very low and the cheater's payoff very high.

Classic Prisoner's Dilemma: The "classic" or "standard" prisoner's dilemma refers to the single-play game with no communication between the players. In the single-play game, defect is a dominant strategy and the equilibrium is defect-defect. The classic prisoner's dilemma is often compared with the multiple play or iterated prisoner's dilemma.

Cooperate: In the standard single-play no communication prisoner's dilemma, actors have a choice between one of two strategies: cooperation or defection. In the standard game, defection is a dominant strategy so actors are not expected to select the cooperation strategy. In an iterated prisoner's dilemma, an actor can adopt many possible strategies, including always cooperate. Cooperation can be a rational strategy (i.e., maximizes payoffs) in an iterated prisoner's dilemma.

Chicken: In the prisoner's dilemma, the preference order of both actors is DC>CC>DD>CD (where D=defect and C=cooperate). A new game is created when the order of the preferences is altered; the new game may have a different equilibrium and dominant strategies. The preference order for the game of chicken is DC>CC>CD>DD; in chicken mutual defection is so awful, a player would rather take the sucker's payoff than be trapped in the defect-defect outcome. Chicken has multiple equilibrium and has been used to model deterrence strategies.

Defect: In the standard single-play no communication prisoner's dilemma, actors have a choice between one of two strategies: cooperation or defection. In the standard game, defection is a dominant strategy so actors are not expected to select the cooperation strategy. In an iterated prisoner's dilemma, an actor can adopt many possible strategies, including always defect.

Discount Rate: A discount rate implies that the value of future payoff is less than a current payoff for the same amount. If someone offered you $100 today or $100 in ten years, you would take the money today, invest it, and have a larger sum in ten years. In the iterated prisoner's dilemma, the higher the discount rate the lower the value of the future; this implies that the higher the discount rate the less likely cooperation will emerge.

Dominant Strategy: A dominant strategy exists if one strategy provides the maximum payoff regardless of the strategy selected by the other player. In the classic prisoner's dilemma, the defect strategy pays the highest amount whether the other player cooperates or defects. Not all games have a dominant strategy. In these instances, the best strategy depends on the strategy selected by the other player.

Equilibrium: The expected outcome in a game. The equilibrium in the classic prisoner's dilemma is "defect-defect". In the game of Chicken, there are two equilibria. According to the Folk Theorem, in the iterated prisoner's dilemma any outcome can become an equilibrium.

Iterated Game: In the classic prisoner's dilemma, the game is played only once. In an iterated game, the game is played many times. Also referred to as a repeated game.

Multiple Equilibria: An equilibrium is the expected outcome in a game. In the classic prisoner's dilemma there is a single equilibrium ("defect-defect"). In other games, there are multiple equilibria. In the game of Chicken, there are two equilibria. According to the Folk Theorem, in the iterated prisoner's dilemma any outcome can become an equilibrium.

Nash Equilibrium: A Nash Equilibrium implies that neither player has an incentive to alter his/her strategy because any unilateral action will decrease his/her payoff. In the classic prisoner's dilemma, the "defect-defect" equilibrium is also a Nash Equilibrium because neither player has an incentive to begin cooperating; unilateral cooperation would shift the player from the third worst payoff to the very worst or sucker's payoff.

Ordinal Payoffs: The most common payoff structure for the prisoner's dilemma employs ordinal payoffs which simply rank the payoffs from best to worse. In contrast, cardinal payoffs involve assigning a value (dollars, utility, etc.) to each payoff. By using cardinal payoffs, intensity of the game can be varied by making the sucker's payoff very low and the cheater's payoff very high.

Payoff: The payoff matrix sets the payoffs for each player and therefore determines the preference order of the actor and the game being played. Payoffs can be ordinal (e.g., 1,2,3,4) or cardinal (e.g., $20, $5, $0, -$10). In the tables, the payoff (4,1) refers to the payoffs for each player (i.e., (player 1, player 2)). In this case, player 1 gets his/her worse outcome and player 2 gets his/her best outcome.

Preference Order: The order of preferred outcomes from a player's perspective. The best outcome is "1"; the worst outcome is "4." The preference order determines the game. In the prisoner's dilemma, both players have a preference order of DC>CC>DD>CD.

Shadow of the Future: The shadow refers to the length of the game in an iterated prisoner's dilemma. The longer the shadow of the future, the more likely it is that cooperation emerges.

Tit-For-Tat (TFT): A strategy used in an iterated prisoner's dilemma. It involves cooperating on the first move and reciprocating on all subsequent moves (i.e., if your partner defects, you punish with a defection). Axelrod (1984) has shown that TFT maximizes payoffs in a multi-player computer tournament. A variant of the TFT, tit-for-two-tats (TF2T) is more forgiving and avoids the potential spirals of defection which can undermine a TFT strategy.

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