Ising model versus normal form game

TL;DR

This paper compares the 2-spin Ising model and 2x2 normal form games, showing how modifications to the Ising model can replicate all game configurations, including Pareto optimality, opening new research avenues.

Contribution

It introduces a new coupling term to the Ising model to fully replicate 2x2 game configurations, bridging statistical mechanics and game theory.

Findings

All Nash equilibria are recoverable by the Ising model.

Adding a coupling term captures Pareto optimal configurations.

A complete bilinear objective function is sufficient for modeling 2x2 games.

Abstract

The 2-spin Ising model in statistical mechanics and the 2x2 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 condiderations are introduced like 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 2x2 game. Using this one-to-one mapping, new perspectives for future research in both fields can be envisioned.