Reciprocal cooperation in the prisoner’s dilemma repeated with random horizon

Abstract

A standard assumption on the Iterated Prisoner’s Dilemma is that the probability of further interaction is constant. Then, cooperation via reciprocity can be guaranteed if and only if this probability is sufficiently high. In this paper, we analyze a more realistic model: a discrete random variable, not necessarily geometric, governs the number of interactions. We obtain necessary conditions and sufficient conditions for reciprocal cooperation based on the use of TFT strategy by both players. The obtained conditions are particularized to classes of distributions with monotonous failure rate and to some relevant probability models.