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 param-eteres. Each agent is governed by a binary Markovian strategy (BMS) specified by 4 conditional probabilities [p R , p S , p T , p P ] that take values 0 or 1. The initial configuration consists in a random assignment of " strategists " among the 2 4 = 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 stochastichally); and iii) the amount of noise measured by a parameter ǫ. However a robust winner strategy is [1,0,1,1].