Evolutionary Markovian Strategies in 2 x 2 Spatial Games

Details Evolutionary Markovian Strategies in 2 x 2 Spatial Games Evolutionary Markovian Strategies in 2 x 2 Spatial Games

2006-06-07

arxiv.org/abs/physics/0606076v1

Physics

Physics and Society

18 pages, 8 figures (7 of these figures contain 4 encapsulapted poscript files each)

Scientific paper

10.1016/j.physa.2006.09.004

Evolutionary spatial 2 x 2 games between heterogeneous agents are analyzed using different variants of cellular automata (CA). Agents play repeatedly against their nearest neighbors 2 x 2 games specified by a rescaled payoff matrix with two parameteres. 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 epsilon. However a robust winner strategy is [1,0,1,1].

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