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Evolution Of Cooperation In A Spatial Prisoner'S Dilemma

Author

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  • FRANK SCHWEITZER

    (Fraunhofer Institute for Autonomous Intelligent Systems, Schloss Birlinghoven, 53754 Sankt Augustin, Germany;
    Institute of Physics, Humboldt University, Invalidenstraße 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 MÜHLENBEIN

    (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.

Suggested Citation

  • Frank Schweitzer & Laxmidhar Behera & Heinz Mühlenbein, 2002. "Evolution Of Cooperation In A Spatial Prisoner'S Dilemma," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 5(02n03), pages 269-299.
    • Handle: RePEc:wsi:acsxxx:v:05:y:2002:i:02n03:n:s0219525902000584
    DOI: 10.1142/S0219525902000584
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    Citations

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    Cited by:

    1. Du, Faqi & Fu, Feng, 2013. "Quantifying the impact of noise on macroscopic organization of cooperation in spatial games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 35-44.
    2. Salatino, Saverio & Di Gregorio, Salvatore, 2015. "A cellular model of prisoners dilemma for “prodding gratuity”," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 214-227.
    3. Matus Halas, 2018. "Balancing Against Threats In Interactions Determined By Distance And Overall Gains," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-22, August.
    4. Jason Barr & Troy Tassier, 2010. "Endogenous Neighborhood Selection and the Attainment of Cooperation in a Spatial Prisoner’s Dilemma Game," Computational Economics, Springer;Society for Computational Economics, vol. 35(3), pages 211-234, March.
    5. Hokky Situngkir & Deni Khanafiah, 2004. "Metabolism of Social System: N-Person Iterated Prisoner’s Dilemma Analysis In Random Boolean Network," Game Theory and Information 0405002, University Library of Munich, Germany.
    6. Yang, Xiqing & Zhang, Feng & Wang, Wanxiong, 2019. "Predation promotes cooperation in Prisoner’s dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 20-24.

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