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Ising model versus normal form game

Author

Listed:
  • Serge Galam

    (CREA - Centre de recherche en épistémologie appliquée - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Bernard Walliser

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

The 2-spin Ising model in statistical mechanics and the 2×2 normal form game in game theory are compared. All configurations allowed by the second are recovered by the first when the only concern is about Nash equilibria. But it holds no longer when Pareto optimum considerations are introduced as in the prisoner's dilemma. This gap can nevertheless be filled by adding a new coupling term to the Ising model, even if that term has up to now no physical meaning. An individual complete bilinear objective function is thus found to be sufficient to reproduce all possible configurations of a 2×2 game. Using this one-to-one mapping new perspectives for future research in both fields can be envisioned.

Suggested Citation

  • Serge Galam & Bernard Walliser, 2010. "Ising model versus normal form game," PSE-Ecole d'économie de Paris (Postprint) halshs-00754481, HAL.
    • Handle: RePEc:hal:pseptp:halshs-00754481
    DOI: 10.1016/j.physa.2009.09.029
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    References listed on IDEAS

    as
    1. Serge Galam, 2008. "Sociophysics: A Review Of Galam Models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 409-440.
    2. Harjoat Singh Bhamra, 2000. "Imitation In Financial Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 473-478.
    3. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    4. Richard Arena & Agnès Festré, 2006. "Knowledge, Beliefs and Economics," Post-Print halshs-00271316, HAL.
    5. Bernard Walliser, 2006. "Justifications of game equilibrium notions," Post-Print halshs-00754735, HAL.
    6. Bernard Walliser, 2006. "Justifications of Game Theoretic Equilibrium Notions," Chapters, in: Richard Arena & Agnès Festré (ed.), Knowledge, Beliefs and Economics, chapter 5, Edward Elgar Publishing.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

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    7. Zimmaro, Filippo & Galam, Serge & Javarone, Marco Alberto, 2024. "Asymmetric games on networks: Mapping to Ising models and bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    8. Colin Benjamin & Arjun Krishnan U.M., 2023. "Nash equilibrium mapping vs. Hamiltonian dynamics vs. Darwinian evolution for some social dilemma games in the thermodynamic limit," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(7), pages 1-16, July.
    9. Paolo Pellizzari & Elena Sartori & Marco Tolotti, 2015. "Optimal Policies In Two-Step Binary Games Under Social Pressure And Limited Resources," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 18(05n06), pages 1-16, August.

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