Optimal transport and Cournot-Nash equilibria

Adrien Blanchet () and Guillaume Carlier ()
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Adrien Blanchet: GREMAQ - Groupe de recherche en économie mathématique et quantitative - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique
Guillaume Carlier: MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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Abstract: We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is not convex in the usual sense in general but it turns out to have hidden strict convexity properties in many relevant cases. This enables us to obtain new uniqueness results and a characterisation of equilibria in terms of some partial differential equations, a simple numerical scheme in dimension one as well as an analysis of the inefficiency of equilibria.

Keywords: optimal transport; Cournot-Nash equilibria; mean-field games; convexity along generalised geodesics; Monge-Amp\ère equations; externalities (search for similar items in EconPapers)
Date: 2015-07-16
Note: View the original document on HAL open archive server: https://hal.science/hal-00712488v1
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Citations: View citations in EconPapers (4)

Published in Mathematics of Operations Research, 2015, 41 (1), pp.125-145. ⟨10.1287/moor.2015.0719⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00712488

DOI: 10.1287/moor.2015.0719

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