Acquired Cooperation in Finite-Horizon Games

When a prisoner’s-dilemma-like game is repeated any finite number of times, 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 late periods in which unilateral defection has become unprofitable. In this case, cooperation may also be attainable in the first period, since defection then can effectively be punished by cessation of cooperation by all the other players. 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 later on, and at the same time, punishments are less effective than at the beginning. These conditions are sufficient for the existence of an equilibrium in which players cooperate in all periods. * We would like to thank Eliakim Katz, with whom the ideas presented in this paper were originally conceived. a E-mail: [email protected] Personal homepage: http://faculty.biu.ac.il/~milchti b E-mail: [email protected] Personal homepage: http://faculty.biu.ac.il/~weissa1