Acquired Cooperation in Finite-Horizon Dynamic Games

Igal Milchtaich and Avi Weiss

Abstract.  No matter how many times a prisoner’s-dilemma-like game is repeated, the only equilibrium outcome is the one in which all players defect in all periods. However, if cooperation among the players changes their perception of the game by making defection increasingly less attractive, then players may be willing to cooperate in the late stages of the repeated interaction, when unilateral defection has become unprofitable. In this case, cooperation may be attainable also in the early stages, since any defection in these stages may be effectively punished by all the other players also ceasing to cooperate. In this paper, we explore this possibility, and consider conditions guaranteeing the players’ willingness to cooperate also in the middle periods, in which defection is more profitable than in the late periods and, at the same time, punishments are less effective than at the beginning. These conditions are sufficient for cooperation in all periods to be an equilibrium outcome.