Evolutionary Markovian strategies in 2×2 spatial games

Evolutionary spatial 2×2 games between heterogeneous agents are analyzed using different variants of cellular automata (CA). Agents play repeatedly against their nearest neighbors 2×2 games specified by a rescaled payoff matrix with two parameters. Each agent is governed by a binary Markovian strategy (BMS) specified by four conditional probabilities [pR, pS, pT, pP] that take values 0 or 1. The initial configuration consists in a random assignment of “strategists” among the 24= 16 possible BMS. The system then evolves within strategy space according to the simple standard rule: each agent copies the strategy of the neighbor who got the highest payoff. Besides on the payoff matrix, the dominant strategy—and the degree of cooperation—depend on (i) the type of the neighborhood (von Neumann or Moore); (ii) the way the cooperation state is actualized (deterministically or stochastically); and (iii) the amount of noise measured by a parameter ε. However a robust winner strategy is [1,0,1,1].