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Prisoner'S Dilemma In One-Dimensional Cellular Automata: Visualization Of Evolutionary Patterns

Author

Listed:
  • MARCELO ALVES PEREIRA

    (Departamento de Física e Matemática, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Av. Bandeirantes, 3900, 14040-901, Ribeirão Preto, SP, Brazil)

  • ALEXANDRE SOUTO MARTINEZ

    (Departamento de Física e Matemática, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Av. Bandeirantes, 3900, 14040-901, Ribeirão Preto, SP, Brazil)

  • AQUINO LAURI ESPÍNDOLA

    (Departamento de Física e Matemática, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Av. Bandeirantes, 3900, 14049-900, Ribeirão Preto, SP, Brazil;
    Departamento de Medicina Social, Faculdade de Medicina de Ribeirão Preto, Universidade de São Paulo, Av. Bandeirantes, 3900, 14049-900, Ribeirão Preto, SP, Brazil)

Abstract

The spatial Prisoner's Dilemma is a prototype model to show the emergence of cooperation in very competitive environments. It considers players, at sites of lattices, that can either cooperate or defect when playing the Prisoner's Dilemma withzother players. This model presents a rich phase diagram. Here we consider players in cells of one-dimensional cellular automata. Each player interacts withzother players. This geometry allows us to vary, in a simple manner, the number of neighbors ranging from one up to the lattice size, including self-interaction. This approach has multiple advantages. It is simple to implement numerically and we are able to retrieve all the results found in the previously considered lattices, with a faster convergence to stationary values. More remarkable, it permits us to keep track of the spatio-temporal evolution of each player of the automaton, giving rise to interesting patterns. These patterns allow the interpretation of cooperation/defection clusters as particles, which can be absorbed and collided among themselves. The presented approach represents a new paradigm to study the emergence and maintenance of cooperation in the spatial Prisoner's Dilemma.

Suggested Citation

  • Marcelo Alves Pereira & Alexandre Souto Martinez & Aquino Lauri Espíndola, 2008. "Prisoner'S Dilemma In One-Dimensional Cellular Automata: Visualization Of Evolutionary Patterns," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 187-201.
  • Handle: RePEc:wsi:ijmpcx:v:19:y:2008:i:01:n:s0129183108012017
    DOI: 10.1142/S0129183108012017
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    References listed on IDEAS

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    1. Metzger, T. & Irawan, A. & Tsotsas, E., 2006. "Remarks on the paper “Extension of Hoshen–Kopelman algorithm to non-lattice environments” by A. Al-Futaisi and T.W. Patzek, Physica A 321 (2003) 665–678," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 558-560.
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