FRANK SCHWEITZER () (Fraunhofer Institute for Autonomous Intelligent Systems, Schloss Birlinghoven, 53754 Sankt Augustin, Germany; Institute of Physics, Humboldt University, InvalidenstraÃe 110, 10115 Berlin, Germany) LAXMIDHAR BEHERA () (Fraunhofer Institute for Autonomous Intelligent Systems, Schloss Birlinghoven, 53754 Sankt Augustin, Germany; Department of Electrical Engineering, Indian Institute of Technology, Kanpur 208 016, India) HEINZ MÃHLENBEIN () (Fraunhofer Institute for Autonomous Intelligent Systems, Schloss Birlinghoven, 53754 Sankt Augustin, Germany)
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 us 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.
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