Evolution of Cooperation in a Spatial Prisoner's Dilemma

Frank Schweitzer; Laxmidhar Behera; Heinz Muehlenbein

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Evolution of Cooperation in a Spatial Prisoner's Dilemma

Frank Schweitzer·Laxmidhar Behera·Heinz Muehlenbein

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Abstract

We investigate the spatial distribution and the global frequency of agents who can either cooperate or defect. The agent interaction is described by a deterministic, non-iterated prisoner's dilemma game, further each agent only locally interacts with his neighbors. Based on a detailed analysis of the local payoff structures we derive critical conditions for the invasion or the spatial coexistence of cooperators and defectors. These results are concluded in a phase diagram that allows to identify five regimes, each characterized by a distinct spatiotemporal dynamics and a corresponding final spatial structure. In addition to the complete invasion of defectors, we find coexistence regimes with either a majority of cooperators in large spatial domains, or a minority of cooperators organized in small non-stationary domains or in small clusters. The analysis further allowed a verification of computer simulation results by Nowak and May (1993). Eventually, we present simulation results of a true 5-person game on a lattice. This modification leads to non-uniform spatial interactions that may even enhance the effect of cooperation. Keywords: Prisoner's dilemma; cooperation; spatial 5-person game

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cond-mat.stat-mech cs.GT nlin.CG

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Frank Schweitzer, Laxmidhar Behera, Heinz Muehlenbein. 2002-11-26. Evolution of Cooperation in a Spatial Prisoner's Dilemma. https://arxiv.org/abs/cond-mat/0211605

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