Finitely Repeated Prisoners' Dilemma Games - Do Players use Backward or Forward Induction?

Abstract

In the one-shot version of the Prisoners' Dilemma (PD) game, individuals pursue mutually destructive strategies (they both defect). The repeated PD examines whether interactions over time can induce players to adopt cooperative strategies. Cooperation is possible in the infinitely repeated PD. However, in the finitely repeated version, backward induction forces immediate mutual defection. Cooperation becomes possible if players are unsure of when the final round will be (Myerson 1991, Brams and Kilgour 2002), or when players are 'absent-minded' regarding the current round of play (Dilger 1998), since players will use forward, rather than backward, induction. In this paper, we develop a model in which cooperation may be sustainable in a finitely repeated PD game, even when players have perfect knowledge of the current round number and final round number. We analyse whether boundedly rational players use backward or forward induction in such a game. Players use forward induction if there are many rounds of play remaining, and the end round is a distant prospect. They only switch to backward induction at a critical round (when the end round is in sight). We believe that the insights of the model are so important for practical conflict scenarios, that they should be tested in an experimental game. In the final section, we suggest specifications for such a game.