Right Type Departmental Bulletin Paper

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 mechan-ics. Moreover, this paper examines the relations, the order parameter, and the action)$s $ probability distribution on the lattice with percolation. As a result, theoretical calculations agree with classical evolutionary game theory in tems of the parameter size. This paper shows that bifurcations occur in a quenched system with extemalities, hence, this system has multiple equilibria. This model applies to a two-player model of reinforcement learning with memory [11]. This paper analyzes Prisoner’s Dilemma Game, shows that this Nash equilibrium is Pareto optimal in terms of the length of memory