Optimal Transport and Cournot-Nash Equilibria

• 成果类型: Article
• 署名作者: Blanchet, Adrien; Carlier, Guillaume
• 署名单位: Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Universite PSL; Universite Paris-Dauphine
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2015.0719
• 发表日期: 2016
• 页码: 125-145
• 关键词: mean-field games; EXISTENCE; continuum; MARKETS; traders; MAPS

摘要

We study a class of games with a continuum of players for which a 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.