Relational Nash equilibrium and interrelationships among relational and rational equilibrium concepts

The author gives a definition of a new equilibrium concept, called relational Nash equilibrium (RNE), incorporating players' attitudes, a social psychological aspect of decision making, into analysis of games in normal form. The author investigates the interrelationship among RNE and relational dominant strategy equilibrium (RDSE) (T. Inohara, Relational dominant strategy equilibrium as a generalization of dominant strategy equilibrium in terms of a social psychological aspect of decision making, European Journal of Operational Research 182 (2007) 856-866), and Nash equilibrium (NE). In particular, the following two facts are verified: (i) RNE includes RDSE under conditions on attitudes and preferences of players and (ii) RNE coincides with NE under conditions on attitudes and preferences of players. Prisoners' dilemma game and chicken game are analyzed as applications of RNE.