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Cooperation in a Multi-Dimensional Local Interaction Model

Author

Listed:
  • Alexander F. Tieman

    (Tinbergen Institute & Free University)

  • Harold Houba

    (Free University)

  • Gerard van der Laan

    (Tinbergen Institute & Free University)

Abstract

We consider a local interaction model with a population on an h dimensional torus, in which in each round of play a random player gets a learning draw. This player plays a k+1 action stage game with players in his neighborhood, compares his own average payoff with the average payoff of the neighbors he played against and updates his action based on this comparison. Individuals use the update rule `Win Cooperate, Lose Defect', a multi-player variant of Tit-for-Tat. We prove that there are exactly k+1 stable states and that all of these can be reached with positive probability, for any dimension h of the torus. Furthermore, we prove that when k+1=2, both stable states will be reached with probability 1/2. For k+1>2 we provide some insight in the probability of reaching each of the stable states by presenting simulation results.

Suggested Citation

  • Alexander F. Tieman & Harold Houba & Gerard van der Laan, 1998. "Cooperation in a Multi-Dimensional Local Interaction Model," Game Theory and Information 9803002, EconWPA.
  • Handle: RePEc:wpa:wuwpga:9803002
    Note: Type of Document - dvi (compiled TeX); prepared on IBM PC - Scientific Workplace 2.5; to print on HP/PostScript; pages: 27 ; figures: included. Tinbergen Institute Discussion Paper
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    References listed on IDEAS

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    Cited by:

    1. Giorgio Fagiolo & Luigi Marengo & Marco Valente, 2004. "Endogenous Networks In Random Population Games," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(2), pages 121-147.

    More about this item

    Keywords

    Evolution; Local Interaction; Cooperation; Prisoner's Dilemma.;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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