The historic-stochastic strategist

The basic aim of this paper is to extend earlier work on assessing the effe ct of considering previous results (history) in the evolutionary dynamics o f the spatial formulation of the Prisoner's Dilemma when players follow one -dimensional strategies. The historic strategist models considered before w ere deterministic, so the choices were fixed by the strategies in an automa tic way. In the present work the strategies do not fix the choices but thei r probabilities. Both synchronous and asynchronous updating schemes have be en taken into account. It is concluded here that the essential results foun d in the deterministic scenario remain valid in a probabilistic context: hi storic memory tends to favor the main features of the initial scenario.