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Cournot-Nash equilibrium and optimal transport in a dynamic setting

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Document pages: 28 pages

Abstract: We consider a large population dynamic game in discrete time. The peculiarityof the game is that players are characterized by time-evolving types, and soreasonably their actions should not anticipate the future values of theirtypes. When interactions between players are of mean-field kind, we relate Nashequilibria for such games to an asymptotic notion of dynamic Cournot-Nashequilibria. Inspired by the works of Blanchet and Carlier for the staticsituation, we interpret dynamic Cournot-Nash equilibria in the light of causaloptimal transport theory. Further specializing to games of potential type, weestablish existence, uniqueness and characterization of equilibria. Moreover wedevelop, for the first time, a numerical scheme for causal optimal transport,which is then leveraged in order to compute dynamic Cournot-Nash equilibria.This is illustrated in a detailed case study of a congestion game.

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