Finite composite games: Equilibria and dynamics

Sylvain  Sorin; Cheng  Wan

doi:10.3934/jdg.2016005

Article Contents

2016, Volume 3, Issue 1: 101-120. Doi: 10.3934/jdg.2016005

This issue Previous Article Local market structure in a Hotelling town Next Article

Finite composite games: Equilibria and dynamics

Sylvain Sorin^1, and
Cheng Wan^2,

1.
Sorbonne Universités, UPMC Univ Paris 06, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Univ Paris Diderot, Sorbonne Paris Cité, F-75005, Paris
2.
Department of Economics, University of Oxford, Nuffield College, New Road, Oxford, OX1 1NF

Received: February 28, 2015

Revised: January 31, 2016

Published: December 2015

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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.

Keywords:

Mathematics Subject Classification: Primary: 91A10, 91A22; Secondary: 91A06, 91A13.

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