Deterministic strategies

Let there be a homogenous population with individuals that are able to recognise a previous interactant and remember some aspects of prior outcomes. If the average chance to meet a given partner more than THETA times in a row is w^THETA (where 0<w<1), then a strategy would be a rule, modifying the behaviour (C or D) according to the history of the interaction so far. Obviously, unconditional defection (ALLD) is still an ESS against single cooperating mutants. But there may be other stable strategies as well. In fact, in the Iterated Prisoner's Dilemma (IPD) no strategy is evolutionarily stable (Boyd and Lorberbaum 1987, Lorberbaum 1994).