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Cournot-Nash equilibrium and optimal transport in a dynamic setting

Acciaio, Beatrice, Veraguas, Julio Backhoff and Jia, Junchao (2021) Cournot-Nash equilibrium and optimal transport in a dynamic setting. SIAM Journal on Control and Optimization, 59 (3). 2273 - 2300. ISSN 0363-0129

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Identification Number: 10.1137/20M1321462

Abstract

We consider a large population dynamic game in discrete time. The peculiarity of the game is that players are characterized by time-evolving types, and so reasonably their actions should not anticipate the future values of their types. When interactions between players are of mean field kind, we relate Nash equilibria for such games to an asymptotic notion of dynamic Cournot-Nash equilibria. Inspired by the works of Blanchet and Carlier for the static situation, we interpret dynamic Cournot-Nash equilibria in the light of causal optimal transport theory. Further specializing to games of potential type, we establish existence, uniqueness, and characterization of equilibria. Moreover we develop, 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.

Item Type: Article
Official URL: https://epubs.siam.org/journal/sjcodc
Additional Information: © 2021 Society for Industrial and Applied Mathematics
Divisions: Mathematics
Statistics
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HB Economic Theory
Date Deposited: 01 Apr 2022 23:13
Last Modified: 31 May 2022 15:33
URI: http://eprints.lse.ac.uk/id/eprint/114574

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