Cooperation, Secret Handshakes, and Imitation in the Prisoners' Dilemma

Abstract

Building on A. J. Robson (1990, J. Theoret. Biol. 144, 379–396), we introduce into the repeated prisoners' dilemma mutants who have the ability to send a (costly) signal, i.e., the “secret handshake,” before each round of the game and to condition their actions on whether or not they observe the same signal from their opponent. We show that as mutation probabilities approach zero in the limit, cooperation occurs a positive fraction of the time. Using simulations to study the behavior of the system with nonzero mutation probabilities, we obtain similar results. Surprisingly, in some cases an increased payoff to unilateral defection actually raises the level of cooperation. Journal of Economic Literature Classification Numbers: C70, C72, D60.