Ising model versus normal form game

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.
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Submitted on : Tuesday, November 20, 2012 - 9:43:28 AM
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Serge Galam, Bernard Walliser. Ising model versus normal form game. Physica A: Statistical Mechanics and its Applications, Elsevier, 2010, 389 (3), pp.481-489. ⟨10.1016/j.physa.2009.09.029⟩. ⟨halshs-00754481⟩

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