2020/02/20 by Beatrice Acciaio, Acciaio, Beatrice, Julio Backhoff‐Veraguas +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Economic theories and models #FOS: Economics and business #FOS: Mathematics #General Economics (econ.GN) #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2002.08786
openalex publication_date 2020/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.