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The geometrical patterns of cooperation evolution in the spatial prisoner's dilemma: An intra-group model

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  • Oliveira dos Santos Soares, Ricardo
  • Martinez, Alexandre Souto

Abstract

The prisoner's dilemma (PD) deals with the behavior conflict between two agents, who can either cooperate (cooperators) or defect. If both agents cooperate (defect), they have a unitary (null) payoff. Otherwise the payoff is T for the defector and null for the cooperator. The temptation T to defect is the only free parameter in the model. Here the agents are represented by the cells of a L×L lattice. The agent behaviors are initially randomly distributed according to an initial proportion of cooperators ρc(0). Each agent has no memory of previous behaviors and plays the PD with his/her eight nearest neighbors. At each generation, the considered agent copies the behavior of those who have secured the highest payoff. Once the PD conflict has been established (1

Suggested Citation

  • Oliveira dos Santos Soares, Ricardo & Martinez, Alexandre Souto, 2006. "The geometrical patterns of cooperation evolution in the spatial prisoner's dilemma: An intra-group model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 823-829.
    • Handle: RePEc:eee:phsmap:v:369:y:2006:i:2:p:823-829
    DOI: 10.1016/j.physa.2006.02.003
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    References listed on IDEAS

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    1. Stauffer, Dietrich, 2004. "Introduction to statistical physics outside physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 1-5.
    2. Bouchaud, Jean-Philippe, 2002. "An introduction to statistical finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(1), pages 238-251.
    3. Galam, Serge, 2004. "Sociophysics: a personal testimony," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 49-55.
    4. Jean-Philippe Bouchaud, 2002. "An introduction to statistical finance," Science & Finance (CFM) working paper archive 313238, Science & Finance, Capital Fund Management.
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    Cited by:

    1. Almeida, Enock & da Silva, Roberto & Martinez, Alexandre Souto, 2014. "Strategies generalization and payoff fluctuation optimization in the iterated ultimatum game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 54-65.
    2. Pedro Ribeiro de Andrade & Antonio Miguel Vieira Monteiro & Gilberto Câmara & Sandra Sandri, 2009. "Games on Cellular Spaces: How Mobility Affects Equilibrium," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-5.
    3. Yokoi, Hiroki & Uehara, Takashi & Sakata, Tomoyuki & Naito, Hiromi & Morita, Satoru & Tainaka, Kei-ichi, 2014. "Evolution of altruism in spatial prisoner’s dilemma: Intra- and inter-cellular interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 361-370.

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