Cooperation, but no reciprocity: Individual strategies in the repeated prisoner's dilemma

摘要

The long-run economic relationships depend on the sustainability of the relationships. The well-known theoretical diversity is robust to impatience, renegotiation, and different notions of equilibrium refinement. However, experimental analysis shows that cooperative equilibria is necessary but not sufficient for emergence of cooperative behavior. BOS and Dal Bo and Frechette (Ref. 2) referred to here as DF, have shown that predictive condition for cooperation exists that depends up on a threshold discount factor. However it is not clear whether this threshold guarantees a certain type of equilibria. The present paper has twofold objective namely, to show that individual strategies are similarly predictable and to provide a strategic interpretation of the BOS-threshold. It is shown that across treatments in four recent experiments on the repeated prisoner's dilemma, strategies have a simple, common structure: cooperate with high probability if both players cooperated in the previous round, with low probability after mutual defection, and with intermediate but equal probabilities if exactly one player cooperated in the previous round -regardless of who had cooperated. Such strategies are called Semi-Grim, that characterize the Markov perfect equilibria (MPEs) in Semi-Grim strategies. The experimental subjects switch to cooperation in round 1 and to Semi-Grim in the continuation simultaneously at a level of discount factor that is roughly equal to where the Semi-Grim MPEs appear and the Semi-Grim MPEs appear as the discount factor crosses the BOS-threshold. (61 refs.)