Finite composite games: Equilibria and dynamics

Sylvain Sorin (1) , Cheng Wan (2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 Department of Economics, University of Oxford (UK)

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.

Domaines: Optimisation et contrôle [math.OC]; Microstructure des marchés [q-fin.TR]; Réseaux et télécommunications [cs.NI]; Recherche opérationnelle [math.OC]

Sylvain Sorin, Cheng Wan. Finite composite games: Equilibria and dynamics. Journal of Dynamics and Games, 2016, 3 (1), pp.101-120. ⟨10.3934/jdg.2016005⟩. ⟨hal-02885860⟩