Cooperation in One-Shot and Two-Shot Simultaneous and Sequential Prisoner’s Dilemmas Under Incomplete and Complete Information

• In Event: 259 - Section on Rationality and Society Paper Session. Rationality and Social Structure

Abstract

Although defection is individually rational behavior in the Prisoner’s Dilemma game (PD), cooperation is frequently observed in the PD. Explaining conditions under which cooperation occurs is therefore a major goal in the social and behavioral sciences. In the present paper we apply a model using the social exchange heuristic, and show that it can explain many behavioral regularities in 1-shot and repeated PDs, played simultaneously or sequentially. The heuristic assumes players obtain a psychological payoff or premium in addition to the material payoffs of the game after mutual cooperation and our model assumes a continuous distribution of players’ premiums. We derive equilibria for 1-shot and 2-shot simultaneous and sequential Prisoner’s Dilemma game, under both incomplete and complete information. We show that cooperation is possible but an inefficiency problem may exist in the sense that not all players who would have preferred to cooperate if the game were one of complete information dare to cooperate under incomplete information. However, in the sequential game only, incomplete information may result in higher efficiency than complete information. We also show that chances of cooperation are higher in sequential games than in simultaneously played games, and higher in 2-shot than in 1-shot games, although 2-shot games have end game effects. In future research we aim to extend our analyses to K-shot games, N-person and network games, and aim to test empirically our predictions on the comparison of one-shot to two-shot PDs, simultaneous to sequential PDs, and games with incomplete to complete information.

Authors

• Jacob Dijkstra, University of Groningen

• Marcel Van Assen, Tilburg University