Prisoner's Dilemma payoffs and the evolution of co-operative preferences

We analyse the evolutionary stability of a preference for reciprocity in the Prisoner's Dilemma. A distingushing and, as we argue, plausible, feature of the analysis is that reciprocal players are not assumed to be able to coordinate on mutual cooperation with probability one. We show how two payoff conditions, one well-known and another new, then become crucial for the evolutionary stability of co-operation. Somewhat paradoxically perhaps, an altruistic preference poses a greater threat to stable cooperation than a self-interested preference.