SPATIALISATION AND GREATER GENEROSITY IN THE STOCHASTIC PRISONERS-DILEMMA

The iterated Prisoner's Dilemma has become the standard model for the evolution of cooperative behavior within a community of egoistic agent s, frequently cited for implications in both sociology and biology. Du e primarily to the work of Axelrod (1980a, 1980b, 1984, 1985), a strat egy of tit for tat (TFT) has established a reputation as being particu larly robust. Nowak and Sigmund (1992) have shown, however, that in a world of stochastic error or imperfect communication, it is not TFT th at finally triumphs in an ecological model based on population percent ages (Axelrod and Hamilton 1981), but 'generous tit for tat' (GTFT), w hich repays cooperation with a probability of cooperation approaching 1 but forgives defection with a probability of 1/3. In this paper, we consider a spatialized instantiation of the stochastic Prisoner's Dile mma, using two-dimensional cellular automata (Wolfram, 1984, 1986; Gut owitz, 1990) to model the spatial dynamics of populations of competing strategies. The surprising result is that in the spatial model it is not GTFT but still more generous strategies that are favored. The opti mal strategy within this spatial ecology appears to be a form of 'bend ing over backwards', which returns cooperation for defection with a pr obability of 2/3 - a rate twice as generous as GTFT.