IDEAS home Printed from https://ideas.repec.org/p/wop/safiwp/01-09-049.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    References listed on IDEAS

    as
    1. Kreps, David M., 1990. "Game Theory and Economic Modelling," OUP Catalogue, Oxford University Press, number 9780198283812.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alioğulları Zeynel Harun & Barlo Mehmet, 2016. "Tenacious Selection of Nash Equilibrium," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(2), pages 633-647, June.
    2. Jarratt, Denise & Ceric, Arnela, 2015. "The complexity of trust in business collaborations," Australasian marketing journal, Elsevier, vol. 23(1), pages 2-12.
    3. Send, Jonas & Serena, Marco, 2022. "An empirical analysis of insistent bargaining," Journal of Economic Psychology, Elsevier, vol. 90(C).
    4. Xiaojun (Gene) Shan & Jun Zhuang, 2014. "Modeling Credible Retaliation Threats in Deterring the Smuggling of Nuclear Weapons Using Partial Inspection---A Three-Stage Game," Decision Analysis, INFORMS, vol. 11(1), pages 43-62, March.
    5. Licht Amir N., 2008. "Social Norms and the Law: Why Peoples Obey the Law," Review of Law & Economics, De Gruyter, vol. 4(3), pages 715-750, December.
    6. van Damme, E.E.C., 1995. "Game theory : The next stage," Other publications TiSEM 7779b0f9-bef5-45c7-ae6b-7, Tilburg University, School of Economics and Management.
    7. Giovanna Devetag & Andreas Ortmann, 2007. "When and why? A critical survey on coordination failure in the laboratory," Experimental Economics, Springer;Economic Science Association, vol. 10(3), pages 331-344, September.
    8. Christian Koboldt, 1996. "Consistent planning, backwards induction, and rule-governed behavior," Constitutional Political Economy, Springer, vol. 7(1), pages 35-48, March.
    9. Hutton, Trevor & Sumaila, Ussif Rashid, 2002. "Natural Resource Accounting And South African Fisheries: A Bio-Economic Assessment Of The West Coast Deep-Sea Hake Fishery With Reference To The Optimal Utilisation And Management Of The Resource," Discussion Papers 18018, University of Pretoria, Center for Environmental Economics and Policy in Africa.
    10. Yu, Yanan & He, Yong & Zhao, Xuan, 2021. "Impact of demand information sharing on organic farming adoption: An evolutionary game approach," Technological Forecasting and Social Change, Elsevier, vol. 172(C).
    11. Ho, Teck-Hua, 1996. "Finite automata play repeated prisoner's dilemma with information processing costs," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 173-207.
    12. Willem Karel M. Brauers & Romualdas Ginevičius, 2009. "Robustness in regional development studies. The case of Lithuania," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 10(2), pages 121-140, February.
    13. Killian J. McCarthy & Frederik van Doorn & Brigitte Unger, 2011. "Tax Competition and the Harmonisation of Corporate Tax Rates in Europe," Chapters, in: Miroslav N. Jovanović (ed.), International Handbook on the Economics of Integration, Volume II, chapter 20, Edward Elgar Publishing.
    14. Plan, Asaf, 2023. "Symmetry in n-player games," Journal of Economic Theory, Elsevier, vol. 207(C).
    15. Steven J. Brams & Walter Mattli, 1993. "Theory of Moves: Overview and Examples," Conflict Management and Peace Science, Peace Science Society (International), vol. 12(2), pages 1-39, February.
    16. Hielscher Stefan & Beckmann Markus, 2009. "Social Entrepreneurship und Ordnungspolitik: Zur Rolle gesellschaftlicher Change Agents am Beispiel des Kruppschen Wohlfahrtsprogramms / Social Entrepreneurship and Ordnungspolitik," ORDO. Jahrbuch für die Ordnung von Wirtschaft und Gesellschaft, De Gruyter, vol. 60(1), pages 435-462, January.
    17. Roberto Weber & Colin Camerer & Marc Knez, 2004. "Timing and Virtual Observability in Ultimatum Bargaining and “Weak Link” Coordination Games," Experimental Economics, Springer;Economic Science Association, vol. 7(1), pages 25-48, February.
    18. Jonas Send & Marco Serena, 2021. "An Empirical Analysis of Stubborn Bargaining," Working Papers tax-mpg-rps-2021-05, Max Planck Institute for Tax Law and Public Finance.
    19. Lawrence Boland, 2002. "Towards a useful methodology discipline," Journal of Economic Methodology, Taylor & Francis Journals, vol. 8(1), pages 3-10.
    20. Tesfatsion, Leigh, 2001. "Introduction to the special issue on agent-based computational economics," Journal of Economic Dynamics and Control, Elsevier, vol. 25(3-4), pages 281-293, March.

    More about this item

    Keywords

    Game theory; learning; Nash equilibrium; chaos; rationality; Hamiltonian dynamics;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wop:safiwp:01-09-049. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thomas Krichel (email available below). General contact details of provider: https://edirc.repec.org/data/epstfus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.