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Chaos in Learning a Simple Two Person Game


  • Yuzuru Sato
  • Eizo Akiyama
  • J. Doyne Farmer


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.

Suggested Citation

  • Yuzuru Sato & Eizo Akiyama & J. Doyne Farmer, 2001. "Chaos in Learning a Simple Two Person Game," Working Papers 01-09-049, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:01-09-049

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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,, revised Feb 2009.
    2. Manfred Nermuth & Carlos Alos-Ferrer, 2003. "A comment on "The selection of preferences through imitation"," Economics Bulletin, AccessEcon, vol. 3(7), pages 1-9.
    3. Michael J. Fox & Jeff S. Shamma, 2013. "Population Games, Stable Games, and Passivity," Games, MDPI, Open Access Journal, vol. 4(4), pages 1-23, October.
    4. Steve Phelps & Wing Lon Ng, 2014. "A Simulation Analysis Of Herding And Unifractal Scaling Behaviour," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 21(1), pages 39-58, January.

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

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