Extending the iterated prisoner's dilemma without synchrony

In biology altruistic behaviour of selfish individuals often can be modelled by the iterated Prisoner's Dilemma game (PD). If the opponents are caught repeatedly in this dilemma reciprocity may lead to cooperative strategies adopted by the individuals. In this article we present results from numerical simulations of the infinitely iterated stochastic alternating PD. First we investigate influences of the memory size on strategies in the alternating two player PD. We show that Firm but Fair is a strong strategy hardly affected by memory size and different values of the temptation to defect. Second we discuss successful strategies in the alternating N player N step memory PD. In this situation we focus on the stability of cooperative strategies and compare the results to experiments of predator inspection by sticklebacks carried out by Milinski and co-workers. (C) 1998 Academic Press Limited.