Finite composite games: Equilibria and dynamics

Sylvain Sorin, Cheng Wan

Published 2015-03-27Version 1

We introduce finite games with the following types of players: (I) nonatomic players, (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 types 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.