Rational Cooperation in the Finitely Repeated Prisoners' Dilemma

Rational Cooperation in the Finitely Repeated Prisoners' Dilemma

1982 | DAVID M. KREPS, PAUL MILGROM, JOHN ROBERTS AND ROBERT WILSON
This paper examines how incomplete information about players' strategies or payoffs can lead to cooperation in finitely repeated prisoner's dilemma games, despite the fact that finking (defecting) at each stage is the only Nash equilibrium. The authors show that if one player is uncertain about the other's rationality or strategy, cooperation can occur. They use the concept of sequential equilibrium to analyze this. The basic game involves N repetitions of a two-player, bimatrix game where each player has a dominant strategy to defect. However, with incomplete information, players may cooperate. The authors consider two models: one where a player is uncertain about the other's strategy (Tit-for-Tat), and another where both players have uncertainty about each other's payoffs. In the first model, if one player (COL) is uncertain whether the other (ROW) is rational, they may cooperate. The authors show that the number of stages where players defect is bounded by a constant depending on the probability of the other player being rational. In the second model, uncertainty about payoffs can also lead to cooperation. The authors argue that cooperation in finitely repeated prisoner's dilemma games can be explained by informational asymmetries and lack of common knowledge. They show that even with rational, self-interested behavior, cooperation can occur if players have incomplete information about each other's strategies or payoffs. The paper concludes that further research is needed to understand the implications of these findings in economic, political, and military contexts.This paper examines how incomplete information about players' strategies or payoffs can lead to cooperation in finitely repeated prisoner's dilemma games, despite the fact that finking (defecting) at each stage is the only Nash equilibrium. The authors show that if one player is uncertain about the other's rationality or strategy, cooperation can occur. They use the concept of sequential equilibrium to analyze this. The basic game involves N repetitions of a two-player, bimatrix game where each player has a dominant strategy to defect. However, with incomplete information, players may cooperate. The authors consider two models: one where a player is uncertain about the other's strategy (Tit-for-Tat), and another where both players have uncertainty about each other's payoffs. In the first model, if one player (COL) is uncertain whether the other (ROW) is rational, they may cooperate. The authors show that the number of stages where players defect is bounded by a constant depending on the probability of the other player being rational. In the second model, uncertainty about payoffs can also lead to cooperation. The authors argue that cooperation in finitely repeated prisoner's dilemma games can be explained by informational asymmetries and lack of common knowledge. They show that even with rational, self-interested behavior, cooperation can occur if players have incomplete information about each other's strategies or payoffs. The paper concludes that further research is needed to understand the implications of these findings in economic, political, and military contexts.
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