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Chaotic and deterministic switching in a two-person game


  • Manuela A. D. Aguiar

    () (Faculdade de Economia, Universidade do Porto)

  • Sofia B. S. D. Castro

    () (Faculdade de Economia, Universidade do Porto)


We study robust long-term complex behaviour in the Rock-Scissors-Paper game with two players, played using reinforcement learning. The complex behaviour is connected to the existence of a heteroclinic network for the dynamics. This network is made of three heteroclinic cycles consisting of nine equilibria and the trajectories connecting them. We provide analytical proof both for the existence of chaotic switching near the heteroclinic network and for the relative asymptotic stability of at least one cycle in the network, leading to behaviour ranging from almost deterministic actions to chaotic-like dynamics. Our results are obtained by making use of the symmetry of the original problem, a new approach in the context of learning.

Suggested Citation

  • Manuela A. D. Aguiar & Sofia B. S. D. Castro, 2008. "Chaotic and deterministic switching in a two-person game," FEP Working Papers 305, Universidade do Porto, Faculdade de Economia do Porto.
  • Handle: RePEc:por:fepwps:305

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    References listed on IDEAS

    1. Berger, Ulrich, 2005. "Fictitious play in 2 x n games," Journal of Economic Theory, Elsevier, vol. 120(2), pages 139-154, February.
    2. Feltovich, Nick, 1999. "Equilibrium and reinforcement learning in private-information games: An experimental study," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1605-1632, September.
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    More about this item


    learning process; dynamics; switching; chaos;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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