IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v280y2000i3p522-553.html
   My bibliography  Save this article

Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact

Author

Listed:
  • Marsili, Matteo
  • Challet, Damien
  • Zecchina, Riccardo

Abstract

We discuss a model of heterogeneous, inductive rational agents inspired by the El Farol Bar problem and the Minority Game. As in markets, agents interact through a collective aggregate variable — which plays a role similar to price — whose value is fixed by all of them. Agents follow a simple reinforcement-learning dynamics where the reinforcement, for each of their available strategies, is related to the payoff delivered by that strategy. We derive the exact solution of the model in the “thermodynamic” limit of infinitely many agents using tools of statistical physics of disordered systems. Our results show that the impact of agents on the market price plays a key role: even though price has a weak dependence on the behavior of each individual agent, the collective behavior crucially depends on whether agents account for such dependence or not. Remarkably, if the adaptive behavior of agents accounts even “infinitesimally” for this dependence they can, in a whole range of parameters, reduce global fluctuations by a finite amount. Both global efficiency and individual utility improve with respect to a “price taker” behavior if agents account for their market impact.

Suggested Citation

  • Marsili, Matteo & Challet, Damien & Zecchina, Riccardo, 2000. "Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 522-553.
    • Handle: RePEc:eee:phsmap:v:280:y:2000:i:3:p:522-553
    DOI: 10.1016/S0378-4371(99)00610-X
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843719900610X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/S0378-4371(99)00610-X?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    3. Johnson, N.F. & Jarvis, S. & Jonson, R. & Cheung, P. & Kwong, Y.R. & Hui, P.M., 1998. "Volatility and agent adaptability in a self-organizing market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 258(1), pages 230-236.
    4. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-411, May.
    5. Challet, Damien & Marsili, Matteo & Zhang, Yi-Cheng, 2000. "Modeling market mechanism with minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 276(1), pages 284-315.
    6. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
    7. Rustichini, A., 1998. "Sophisticated Players and Sophisticated Agents," Discussion Paper 1998-110, Tilburg University, Center for Economic Research.
    8. Rustichini, Aldo, 1999. "Optimal Properties of Stimulus--Response Learning Models," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 244-273, October.
    9. G. Caldarelli & M. Marsili & Y. -C. Zhang, 1997. "A Prototype Model of Stock Exchange," Papers cond-mat/9709118, arXiv.org.
    10. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    11. W. Brian Arthur, 1994. "Inductive Reasoning, Bounded Rationality and the Bar Problem," Working Papers 94-03-014, Santa Fe Institute.
    12. Rustichini, A., 1998. "Sophisticated Players and Sophisticated Agents," Other publications TiSEM de5b9fc1-8021-4255-8a80-5, Tilburg University, School of Economics and Management.
    13. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    14. 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.
    15. Aumann, Robert J., 1997. "Rationality and Bounded Rationality," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 2-14, October.
    16. Challet, Damien & Zhang, Yi-Cheng, 1998. "On the minority game: Analytical and numerical studies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(3), pages 514-532.
    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. Kets, W., 2007. "The Minority Game : An Economics Perspective," Other publications TiSEM 65d52a6a-b27d-45a9-93a7-e, Tilburg University, School of Economics and Management.
    2. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    3. Wawrzyniak, Karol & Wiślicki, Wojciech, 2012. "Mesoscopic approach to minority games in herd regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2056-2082.
    4. Paolo Laureti & Peter Ruch & Joseph Wakeling & Yi-Cheng Zhang, 2004. "The Interactive Minority Game: a Web based investigation of human market interactions," Experimental 0402004, University Library of Munich, Germany.
    5. Pierre Coucheney & Bruno Gaujal & Panayotis Mertikopoulos, 2015. "Penalty-Regulated Dynamics and Robust Learning Procedures in Games," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 611-633, March.
    6. Liu, Jinzhuo & Meng, Haoran & Wang, Wei & Li, Tong & Yu, Yong, 2018. "Synergy punishment promotes cooperation in spatial public good game," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 214-218.
    7. Semeshenko, Viktoriya & Gordon, Mirta B. & Nadal, Jean-Pierre, 2008. "Collective states in social systems with interacting learning agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4903-4916.
    8. Groot, Robert D. & Musters, Pieter A.D., 2005. "Minority Game of price promotions in fast moving consumer goods markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 533-547.

    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. Kets, W., 2007. "The Minority Game : An Economics Perspective," Other publications TiSEM 65d52a6a-b27d-45a9-93a7-e, Tilburg University, School of Economics and Management.
    2. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    3. 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.
    4. Mansilla, R, 2000. "From naive to sophisticated behavior in multiagents-based financial market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 478-488.
    5. Chmura, Thorsten & Pitz, Thomas, 2004. "Minority Game: Experiments and Simulations of Traffic Scenarios," Bonn Econ Discussion Papers 23/2004, University of Bonn, Bonn Graduate School of Economics (BGSE).
    6. Andersen, Jørgen Vitting & de Peretti, Philippe, 2021. "Heuristics in experiments with infinitely large strategy spaces," Journal of Business Research, Elsevier, vol. 129(C), pages 612-620.
    7. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    8. Arthur Charpentier & Romuald Elie & Carl Remlinger, 2020. "Reinforcement Learning in Economics and Finance," Papers 2003.10014, arXiv.org.
    9. Jørgen Vitting Andersen & Philippe de Peretti, 2020. "Heuristics in experiments with infinitely large strategy spaces," Post-Print hal-02435934, HAL.
    10. Epstein, Daniel & Bazzan, Ana L.C., 2013. "The value of less connected agents in Boolean networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5387-5398.
    11. 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.
    12. V. P. Crawford, 2014. "Boundedly rational versus optimization-based models of strategic thinking and learning in games," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 5.
    13. Jørgen Vitting Andersen & Philippe de Peretti, 2020. "Heuristics in experiments with infinitely large strategy spaces," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02435934, HAL.
    14. Vee-Liem Saw & Lock Yue Chew, 2020. "No-boarding buses: Synchronisation for efficiency," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-34, March.
    15. Panayotis Mertikopoulos & William H. Sandholm, 2016. "Learning in Games via Reinforcement and Regularization," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1297-1324, November.
    16. 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.
    17. Matteo Marsili & Damien Challet, 2001. "Trading Behavior And Excess Volatility In Toy Markets," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 3-17.
    18. Płatkowski, Tadeusz & Ramsza, Michał, 2003. "Playing minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 726-734.
    19. Linde, Jona & Gietl, Daniel & Sonnemans, Joep & Tuinstra, Jan, 2023. "The effect of quantity and quality of information in strategy tournaments," Journal of Economic Behavior & Organization, Elsevier, vol. 211(C), pages 305-323.
    20. J{o}rgen Vitting Andersen & Philippe de Peretti, 2020. "Heuristics in experiments with infinitely large strategy spaces," Papers 2005.02337, arXiv.org.

    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:eee:phsmap:v:280:y:2000:i:3:p:522-553. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.