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Chaos in Learning a Simple Two Person Game

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Author Info

  • Yuzuru Sato
  • Eizo Akiyama
  • J. Doyne Farmer

Abstract

We investigate the problem of learning to play a generalized rock-paper-scissors game. Each player attempts to improve her average score by adjusting the frequency of the three possible responses. For the zero-sum case the learning process displays Hamiltonian chaos. The learning trajectory can be simple or complex, depending on initial conditions. For the non-zero-sum case it shows chaotic transients. This is the first demonstration of chaotic behavior for learning in a basic two person game. As we argue here, chaos provides an important self-consistency condition for determining when adaptive players will learn to behave as though they were fully rational.

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Bibliographic Info

Paper provided by Santa Fe Institute in its series Working Papers with number 01-09-049.

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Date of creation: Sep 2001
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Handle: RePEc:wop:safiwp:01-09-049

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Related research

Keywords: Game theory; learning; Nash equilibrium; chaos; rationality; Hamiltonian dynamics;

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Cited by:
  1. Cherkashin, Dmitriy & Farmer, J. Doyne & Lloyd, Seth, 2009. "The reality game," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1091-1105, May.
    • Dmitriy Cherkashin & J. Doyne Farmer & Seth Lloyd, 2009. "The Reality Game," Papers 0902.0100, arXiv.org, revised Feb 2009.
  2. Carlos Alós-Ferrer & Manfred Nermuth, 2002. "A Comment on "The Selection of Preferences Through Imitation"," Vienna Economics Papers 0207, University of Vienna, Department of Economics.

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