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Optimal transport and Cournot-Nash equilibria

Blanchet, Adrien; Carlier, Guillaume (2016), Optimal transport and Cournot-Nash equilibria, Mathematics of Operations Research, 41, 3, p. 125-145. 10.1287/moor.2015.0719

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1206.6571v1
Date
2016
Journal name
Mathematics of Operations Research
Volume
41
Number
3
Publisher
Institute of Management Sciences
Published in
Paris
Pages
125-145
Publication identifier
10.1287/moor.2015.0719
Metadata
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Author(s)
Blanchet, Adrien
Carlier, Guillaume
Abstract (EN)
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.
Subjects / Keywords
convexity along generalised geodesics; Monge-Ampère equations; externalities; Cournot-Nash equilibria; optimal transport; mean-field games

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