Finite composite games: Equilibria and dynamics

TL;DR

This paper analyzes finite composite games involving different participant types, exploring their equilibria and dynamics, with a focus on potential games and congestion scenarios, extending classical results to more complex multi-category settings.

Contribution

It introduces the concept of composite games with mixed participant categories and extends existing equilibrium and dynamic properties to these complex settings.

Findings

Characterization of equilibria via variational inequalities

Extension of potential game properties to composite games

Analysis of evolutionary dynamics in multi-category participant settings

Abstract

We study games with finitely many participants, each having finitely many choices. We consider the following categories of participants: (I) populations: sets of nonatomic agents, (II) atomic splittable players, (III) atomic non splittable players. We recall and compare the basic properties, expressed through variational inequalities, concerning equilibria, potential games and dissipative games, as well as evolutionary dynamics. Then we consider composite games where the three categories of participants are present, a typical example being congestion games, and extend the previous properties of equilibria and dynamics. Finally we describe an instance of composite potential game.