Emergence of observable rules in a spatial game system

Abstract

This study focuses on player’s strategies observed from outside our original spatial game iterated by players, each of which is placed in a lattice site on a two-dimensional square lattice. A particularity of the game lies in the fact that a player’s strategy is not given, but is constructed dynamically in response to the spatial pattern of the player’s actions. This means that the strategy can evolve in time. However, the simulations revealed unexpected results. It was found that all the strategies observed from outside did not evolve, but were fixed in time. This article enumerates all the observed strategies in detail, and examines their characteristics.