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

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  • 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
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    References listed on IDEAS

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    1. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    2. 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.
    3. Franke, Reiner, 2003. "Reinforcement learning in the El Farol model," Journal of Economic Behavior & Organization, Elsevier, vol. 51(3), pages 367-388, July.
    4. 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.
    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.
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    Blog mentions

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    1. The El Farol problem goes digital
      by Diane Coyle in The Enlightened Economist on 2015-05-13 13:51:47

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    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.
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    4. Benjamin Patrick Evans & Mikhail Prokopenko, 2022. "Bounded strategic reasoning explains crisis emergence in multi-agent market games," Papers 2206.05568, arXiv.org.

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