Game Dynamics for Players with Social and Material Preferences

We consider the dynamics, existence and stability of the equilibrium states for large populations of individuals who can play various types of non--cooperative games. The players imitate the most attractive strategies, and the choice is motivated not only by the material payoffs of the strategies, but also by their popularity in the population. The parameter which determines the weights of both factors in the equilibrium states has the same analytical form for all types of considered games, and is identified with the sensitivity to reinforcements parameter in the Hernstein's Matching Law. We prove theorems of existence and uniqueness, and discuss examples of multiple locally stable polymorphic equilibria for the considered types of games.