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Chaotic and deterministic switching in a two-person game

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  • Manuela A. D. Aguiar

    ()
    (Faculdade de Economia, Universidade do Porto)

  • Sofia B. S. D. Castro

    ()
    (Faculdade de Economia, Universidade do Porto)

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    Abstract

    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.

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    File URL: http://www.fep.up.pt/investigacao/workingpapers/08.12.19_wp305.pdf
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    Bibliographic Info

    Paper provided by Universidade do Porto, Faculdade de Economia do Porto in its series FEP Working Papers with number 305.

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    Length: 22 pages
    Date of creation: Dec 2008
    Date of revision:
    Handle: RePEc:por:fepwps:305

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    Related research

    Keywords: learning process; dynamics; switching; chaos;

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