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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. 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.
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    2. Sarkar, Shubhayan & Benjamin, Colin, 2019. "Entanglement renders free riding redundant in the thermodynamic limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 607-613.
    3. Király, Balázs, 2023. "A tensor renormalization group analysis of the Blume–Capel model inspired by game theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    4. Szabó, György & Hódsági, Kristóf, 2016. "The role of mixed strategies in spatial evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 198-206.
    5. 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).
    6. 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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    8. Marco Alberto Javarone, 2016. "Modeling Poker Challenges by Evolutionary Game Theory," Games, MDPI, vol. 7(4), pages 1-10, December.
    9. 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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