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].