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Cooperative equilibria in the finite iterated prisoner's dilemma


  • Kae Nemoto

    (National Institute of Informatics, Japan)

  • Michael J Gagen

    (Institute for Molecular Bioscience, University of Queensland)


Nash equilibria are defined using uncorrelated behavioural or mixed joint probability distributions effectively assuming that players of bounded rationality must discard information to locate equilibria. We propose instead that rational players will use all the information available in correlated distributions to constrain payoff function topologies and gradients to generate novel 'constrained' equilibria, each one a backwards induction pathway optimizing payoffs in the constrained space. In the finite iterated prisoner's dilemma, we locate constrained equilibria maximizing payoffs via cooperation additional to the unconstrained (Nash) equilibrium maximizing payoffs via defection. Our approach clarifies the usual assumptions hidden in backwards induction.

Suggested Citation

  • Kae Nemoto & Michael J Gagen, 2004. "Cooperative equilibria in the finite iterated prisoner's dilemma," Game Theory and Information 0404001, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0404001
    Note: Type of Document - pdf; pages: 15

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    finite iterated prisoner's dilemma; Nash equilibria; constrained optimization; backwards induction; expected payoff ensemble;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis


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