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Evolutionary analysis of a simple Minority Game: Coexistence, dominance, and paradoxical outcomes

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  • Fernandes, Guilherme
  • Wardil, Lucas

Abstract

The Minority Game models the El Farol Bar problem, where individuals decide whether to attend the bar based on expected crowd size. Despite extensive study, the interactions between specific strategies remain underexplored due to the model’s complexity. In this work, we analyze a simplified version of the Minority Game where each player follows a fixed strategy based solely on the outcome of the last winning action. We demonstrate that the long-term population dynamics is determined by two key inequalities that are defined in terms of the number of strategies in the population. Using an evolutionary framework with a death-and-birth process, we perform an invasion analysis to study how a single mutant strategy interacts with a resident population. Our results reveal two possible evolutionary outcomes: stable coexistence of competing strategies or dominance of one strategy, which paradoxically leads to its own disadvantage by becoming the majority. However, by extending our evolutionary analysis to the full set of strategies, we demonstrate that evolutionary dynamics consistently drive the system toward the coexistence of two strategies, preventing the paradoxical outcome.

Suggested Citation

  • Fernandes, Guilherme & Wardil, Lucas, 2025. "Evolutionary analysis of a simple Minority Game: Coexistence, dominance, and paradoxical outcomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 669(C).
  • Handle: RePEc:eee:phsmap:v:669:y:2025:i:c:s0378437125002444
    DOI: 10.1016/j.physa.2025.130592
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    1. Yusuf Mercan & Benjamin Schoefer & Petr Sedláček, 2024. "A Congestion Theory of Unemployment Fluctuations," American Economic Journal: Macroeconomics, American Economic Association, vol. 16(1), pages 238-285, January.
    2. 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.
    3. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-411, May.
    4. 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.
    5. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
    6. Giorgio Fagiolo & Marco Valente, 2005. "Minority Games, Local Interactions, and Endogenous Networks," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 41-57, February.
    7. Park, Daehyeon & Ryu, Doojin & Webb, Robert I., 2024. "Fear of missing out and market stability: A networked minority game approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).
    8. W. Brian Arthur, 1994. "Inductive Reasoning, Bounded Rationality and the Bar Problem," Working Papers 94-03-014, Santa Fe Institute.
    9. Kirley, Michael, 2006. "Evolutionary minority games with small-world interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 521-528.
    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.
    11. 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.
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