A Note on Dynamical Behaviors of a Spatial Game Operated on Intercrossed Rules

Abstract

The present study discusses a twist in hierarchical rules embedded in a spatial game system. In the typical spatial games, each player has its own strategy, and determines its action on the strategy; its action does not determine its strategy. On the dominance relationship between rules, the strategy is an upper-level rule against the action. This means the game has a hierarchy on rules. The present study in order to discuss a twist between rules, introduced a rule determining a player’s strategy from its immediate neighbor’s actions. This introduction results in not to decide which of a strategy and an action is placed in an upper-level. The present paper reports the results about dynamical behaviors observed in a spatial game system with a twist in its hierarchical rules.