Statistical Mechanics of Games - Evolutionary Game Theory -

This paper formulates evolutionary game theory with a new concept using statistical mechanics. This study analyzes the following situations: each player on the lattice plays a game with its nearest neighbor or with a randomly matched player. These situations are formulated using an analogy with the Ising model and the Sherrington-Kirkpatrick model, the simplest models in statistical mechanics. As a result, theoretical calculations agree with classical evolutionary game theory in terms of the parameter size. This paper shows that bifurcations occur in a quenched system with externalities, hence, this system has multiple equilibria. This paper discusses the simplified Cont and Bouchaud model through our models. We extend the player's behavior and matching in Cont and Bouchaud model.