Game Dynamics for Players with Social and Material Preferences

• Main Authors: Platkowski, Tadeusz, Zakrzewski, Jan
• Format: Journal Article
• Language: English
• Published: 30-03-2012
• Subjects: Computer Science - Computer Science and Game Theory; Physics - Adaptation and Self-Organizing Systems
• DOI: 10.48550/arxiv.1203.6749

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.