Reconsidering the Foole's Rejoinder: Backward Induction in Indefinitely Iterated Prisoner's Dilemmas

Abstract

According to the so called “Folk Theorem” for repeated games, stable cooperative relations can be sustained in a Prisoner’s Dilemma if the game is repeated an indefinite number of times. This result depends on the possibility of applying strategies that are based on reciprocity, i.e. strategies that reward cooperation with subsequent cooperation and punish defection with subsequent defection. If future interactions are sufficiently important, i.e. if the discount rate is relatively small, each agent may be motivated to cooperate by fear of retaliation in the future.