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Chaos in Learning a Simple Two Person Game

Author

Listed:
  • 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.

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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    References listed on IDEAS

    as
    1. Kreps, David M., 1990. "Game Theory and Economic Modelling," OUP Catalogue, Oxford University Press, number 9780198283812.
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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. 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. Platkowski, Tadeusz & Zakrzewski, Jan, 2011. "Asymptotically stable equilibrium and limit cycles in the Rock–Paper–Scissors game in a population of players with complex personalities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4219-4226.
    4. Michael J. Fox & Jeff S. Shamma, 2013. "Population Games, Stable Games, and Passivity," Games, MDPI, vol. 4(4), pages 1-23, October.
    5. 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.
    6. Manfred Nermuth & Carlos Alos-Ferrer, 2003. "A comment on "The selection of preferences through imitation"," Economics Bulletin, AccessEcon, vol. 3(7), pages 1-9.
    7. Jakub Bielawski & Thiparat Chotibut & Fryderyk Falniowski & Michal Misiurewicz & Georgios Piliouras, 2022. "Unpredictable dynamics in congestion games: memory loss can prevent chaos," Papers 2201.10992, arXiv.org, revised Jan 2022.
    8. John Realpe-Gómez & Daniele Vilone & Giulia Andrighetto & Luis G. Nardin & Javier A. Montoya, 2018. "Learning Dynamics and Norm Psychology Supports Human Cooperation in a Large-Scale Prisoner’s Dilemma on Networks," Games, MDPI, vol. 9(4), pages 1-14, November.

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    More about this item

    Keywords

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