IDEAS home Printed from https://ideas.repec.org/p/edn/esedps/186.html
   My bibliography  Save this paper

The El Farol Bar Problem Revisited: Reinforcement Learning in a Potential Game

Author

Listed:
  • Duncan Whitehead

Abstract

We revisit the El Farol bar problem developed by Brian W. Arthur (1994) to investigate how one might best model bounded rationality in economics. We begin by modelling the El Farol bar problem as a market entry game and describing its Nash equilibria. Then, assuming agents are boundedly rational in accordance with a reinforcement learning model, we analyse long-run behaviour in the repeated game. We then state our main result. In a single population of individuals playing the El Farol game, learning theory predicts that the population is eventually subdivided into two distinct groups: those who invariably go to the bar and those who almost never do. In doing so we demonstrate that learning theory predicts sorting in the El Farol bar problem.

Suggested Citation

  • Duncan Whitehead, 2008. "The El Farol Bar Problem Revisited: Reinforcement Learning in a Potential Game," Edinburgh School of Economics Discussion Paper Series 186, Edinburgh School of Economics, University of Edinburgh.
    • Handle: RePEc:edn:esedps:186
    as

    Download full text from publisher

    File URL: http://www.econ.ed.ac.uk/papers/id186_esedps.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ann M. Bell & William A. Sethares, 1999. "The El Farol Problem and the Internet: Congestion and Coordination Failure," Computing in Economics and Finance 1999 812, Society for Computational Economics.
    2. Franke, Reiner, 2003. "Reinforcement learning in the El Farol model," Journal of Economic Behavior & Organization, Elsevier, vol. 51(3), pages 367-388, July.
    3. Challet, Damien & Marsili, M & Ottino, Gabriele, 2004. "Shedding light on El Farol," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 469-482.
    4. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    5. Duffy, John & Hopkins, Ed, 2005. "Learning, information, and sorting in market entry games: theory and evidence," Games and Economic Behavior, Elsevier, vol. 51(1), pages 31-62, April.
    6. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-411, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. The El Farol problem goes digital
      by Diane Coyle in The Enlightened Economist on 2015-05-13 13:51:47

    Citations

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


    Cited by:

    1. Shu-Heng Chen & Umberto Gostoli, 2011. "Agent-Based Modeling of the El Farol Bar Problem," ASSRU Discussion Papers 1120, ASSRU - Algorithmic Social Science Research Unit.
    2. Shu-Heng Chen & Umberto Gostoli, 2017. "Coordination in the El Farol Bar problem: The role of social preferences and social networks," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(1), pages 59-93, April.
    3. Paul Karaenke & Martin Bichler & Stefan Minner, 2019. "Coordination Is Hard: Electronic Auction Mechanisms for Increased Efficiency in Transportation Logistics," Management Science, INFORMS, vol. 65(12), pages 5884-5900, December.
    4. Benjamin Patrick Evans & Mikhail Prokopenko, 2022. "Bounded strategic reasoning explains crisis emergence in multi-agent market games," Papers 2206.05568, arXiv.org.

    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. Shu-Heng Chen & Umberto Gostoli, 2017. "Coordination in the El Farol Bar problem: The role of social preferences and social networks," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(1), pages 59-93, April.
    2. Kets, W. & Voorneveld, M., 2007. "Congestion, Equilibrium and Learning : The Minority Game," Other publications TiSEM 49539a1f-2921-4dd9-83a0-4, Tilburg University, School of Economics and Management.
    3. Duffy, John, 2006. "Agent-Based Models and Human Subject Experiments," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 19, pages 949-1011, Elsevier.
    4. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    5. Shu-Heng Chen & Umberto Gostoli, 2011. "Agent-Based Modeling of the El Farol Bar Problem," ASSRU Discussion Papers 1120, ASSRU - Algorithmic Social Science Research Unit.
    6. Arthur Charpentier & Romuald Élie & Carl Remlinger, 2023. "Reinforcement Learning in Economics and Finance," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 425-462, June.
    7. Pietro Dindo & Jan Tuinstra, 2011. "A Class of Evolutionary Models for Participation Games with Negative Feedback," Computational Economics, Springer;Society for Computational Economics, vol. 37(3), pages 267-300, March.
    8. Arthur Charpentier & Romuald Elie & Carl Remlinger, 2020. "Reinforcement Learning in Economics and Finance," Papers 2003.10014, arXiv.org.
    9. Alan Kirman & François Laisney & Paul Pezanis-Christou, 2023. "Relaxing the symmetry assumption in participation games: a specification test for cluster-heterogeneity," Experimental Economics, Springer;Economic Science Association, vol. 26(4), pages 850-878, September.
    10. Gian Italo Bischi & Ugo Merlone, 2017. "Evolutionary minority games with memory," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 859-875, November.
    11. Benjamin Patrick Evans & Mikhail Prokopenko, 2021. "Bounded rationality for relaxing best response and mutual consistency: The Quantal Hierarchy model of decision-making," Papers 2106.15844, arXiv.org, revised Mar 2023.
    12. Linde, Jona & Sonnemans, Joep & Tuinstra, Jan, 2014. "Strategies and evolution in the minority game: A multi-round strategy experiment," Games and Economic Behavior, Elsevier, vol. 86(C), pages 77-95.
    13. Giovanna Devetag & Francesca Pancotto & Thomas Brenner, 2011. "The Minority Game Unpacked: Coordination and Competition in a Team-based Experiment," LEM Papers Series 2011/18, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    14. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
    15. Giulio Bottazzi & Giovanna Devetag, 2002. "Coordination and self-organization in minority games: experimental evidence," CEEL Working Papers 0215, Cognitive and Experimental Economics Laboratory, Department of Economics, University of Trento, Italia.
    16. Masiliūnas, Aidas, 2023. "Learning in rent-seeking contests with payoff risk and foregone payoff information," Games and Economic Behavior, Elsevier, vol. 140(C), pages 50-72.
    17. Matzke, Christina & Challet, Damien, 2008. "Taking a shower in Youth Hostels: risks and delights of heterogeneity," Bonn Econ Discussion Papers 1/2008, University of Bonn, Bonn Graduate School of Economics (BGSE).
    18. Willemien Kets, 2007. "The minority game: An economics perspective," Papers 0706.4432, arXiv.org.
    19. Hopkins, Ed & Posch, Martin, 2005. "Attainability of boundary points under reinforcement learning," Games and Economic Behavior, Elsevier, vol. 53(1), pages 110-125, October.
    20. Challet, Damien, 2008. "Inter-pattern speculation: Beyond minority, majority and $-games," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 85-100, January.

    More about this item

    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:edn:esedps:186. 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: Research Office (email available below). General contact details of provider: https://edirc.repec.org/data/deediuk.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.