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

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  • 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.

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  • 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
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    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. 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.
    3. 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.
    4. 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.
    5. Mendes, R.Vilela, 2001. "Structure-generating mechanisms in agent-based models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 537-561.
    6. 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.
    7. Wen-Juan Xu & Li-Xin Zhong, 2022. "Market impact shapes competitive advantage of investment strategies in financial markets," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-23, February.
    8. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    9. Lucas Fievet & Didier Sornette, 2018. "Calibrating emergent phenomena in stock markets with agent based models," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-17, March.
    10. 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.
    11. 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.
    12. Vincent Ragel & Damien Challet, 2024. "Consistent time travel for realistic interactions with historical data: reinforcement learning for market making," Papers 2408.02322, arXiv.org, revised Jan 2025.

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