Game Dynamics for Players with Social and Material Preferences

TL;DR

This paper studies the dynamics, stability, and equilibrium states of large populations playing non-cooperative games, considering social influences and material payoffs, with implications for understanding strategic behavior in social contexts.

Contribution

It introduces a unified analytical framework for equilibrium analysis in population games incorporating social and material preferences, including existence, uniqueness, and stability results.

Findings

Existence and uniqueness theorems for equilibrium states.

Identification of a common parameter linking social and material influences.

Examples of multiple stable polymorphic equilibria.

Abstract

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.