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Ising model versus normal form game

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  • Galam, Serge
  • Walliser, Bernard

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

  • Galam, Serge & Walliser, Bernard, 2010. "Ising model versus normal form game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 481-489.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:3:p:481-489
    DOI: 10.1016/j.physa.2009.09.029
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    1. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    2. 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.
    3. 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.
    4. Bernard Walliser, 2006. "Justifications of game equilibrium notions," Post-Print halshs-00754735, HAL.
    5. 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.
    6. Richard Arena & Agnès Festré, 2006. "Knowledge, Beliefs and Economics," Post-Print halshs-00271316, HAL.
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    Cited by:

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    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.

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