The paper "Rational Cooperation in the Finitely Repeated Prisoners' Dilemma" by David M. Kreps, Paul Milgrom, John Roberts, and Robert Wilson explores why players in repeated prisoners' dilemma games often cooperate, despite the Nash equilibrium being dominated by defection. The authors attribute this cooperation to incomplete information and reputation effects. They introduce two models to demonstrate how such information asymmetries can lead to significant cooperation: 1. **Model 1: Incomplete Information about Tit-for-Tat Strategy** - One player (COL) is uncertain about the other player's (ROW) strategy, with a small probability that ROW follows the Tit-for-Tat strategy. The authors show that in any sequential equilibrium, the number of rounds where defection occurs is bounded by a constant depending on the probability of ROW being a Tit-for-Tat player. This leads to cooperation in most rounds, except for the last few. 2. **Model 2: Two-Sided Uncertainty about Stage Payoffs** - Both players entertain a small probability that their opponent "enjoys" cooperation. This model also supports cooperation in most rounds, provided there is two-sided uncertainty and the players hypothesize each other will cooperate. The authors conclude that these models illustrate how rational, self-interested behavior can lead to cooperation in finitely repeated prisoners' dilemma games through the mechanisms of incomplete information and reputation effects.The paper "Rational Cooperation in the Finitely Repeated Prisoners' Dilemma" by David M. Kreps, Paul Milgrom, John Roberts, and Robert Wilson explores why players in repeated prisoners' dilemma games often cooperate, despite the Nash equilibrium being dominated by defection. The authors attribute this cooperation to incomplete information and reputation effects. They introduce two models to demonstrate how such information asymmetries can lead to significant cooperation: 1. **Model 1: Incomplete Information about Tit-for-Tat Strategy** - One player (COL) is uncertain about the other player's (ROW) strategy, with a small probability that ROW follows the Tit-for-Tat strategy. The authors show that in any sequential equilibrium, the number of rounds where defection occurs is bounded by a constant depending on the probability of ROW being a Tit-for-Tat player. This leads to cooperation in most rounds, except for the last few. 2. **Model 2: Two-Sided Uncertainty about Stage Payoffs** - Both players entertain a small probability that their opponent "enjoys" cooperation. This model also supports cooperation in most rounds, provided there is two-sided uncertainty and the players hypothesize each other will cooperate. The authors conclude that these models illustrate how rational, self-interested behavior can lead to cooperation in finitely repeated prisoners' dilemma games through the mechanisms of incomplete information and reputation effects.