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The Interplay between Analytics and Computation in the Study of Congestion Externalities: The Case of the El Farol Problem

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  • Eduardo Zambrano

Abstract

In this paper I study the El Farol problem, a deterministic, boundedly rational, multi‐agent model of a resource subject to congestion externalities that was initially studied computationally by Arthur (1994). I represent the interaction as a game, compute the set of Nash equilibria in mixed strategies of this game, and show analytically how the method of inductive inference employed by the agents in Arthur's computer simulation leads the empirical distribution of aggregate attendance to be like those in the set of Nash equilibria of the game. This set contains only completely mixed strategy profiles, which explains why aggregate attendance appears random in the computer simulation even though its set‐up is completely deterministic.

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  • Eduardo Zambrano, 2004. "The Interplay between Analytics and Computation in the Study of Congestion Externalities: The Case of the El Farol Problem," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 6(2), pages 375-395, May.
    • Handle: RePEc:bla:jpbect:v:6:y:2004:i:2:p:375-395
    DOI: 10.1111/j.1467-9779.2004.00170.x
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    References listed on IDEAS

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    1. Sergiu Hart & Andreu Mas-Colell, 2013. "A General Class Of Adaptive Strategies," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 3, pages 47-76, World Scientific Publishing Co. Pte. Ltd..
    2. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
    3. J. Doyne Farmer, 2000. "Physicists Attempt To Scale The Ivory Towers Of Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 311-333.
    4. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    5. W. Brian Arthur, 1994. "Inductive Reasoning, Bounded Rationality and the Bar Problem," Working Papers 94-03-014, Santa Fe Institute.
    6. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    7. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-411, May.
    8. Eduardo Zambrano, 1997. "The Revelation Principle of Bounded Rationality," Research in Economics 97-06-060e, Santa Fe Institute.
    9. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-179, March.
    10. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 407-418.
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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.
    2. Sharif, Omor & Huynh, Nathan & Vidal, Jose M., 2011. "Application of El Farol model for managing marine terminal gate congestion," Research in Transportation Economics, Elsevier, vol. 32(1), pages 81-89.
    3. Dindo, P.D.E. & Tuinstra, J., 2006. "A Behavioral Model for Participation Games with Negative Feedback," CeNDEF Working Papers 06-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    4. 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.

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