SIAM Journal on Control and Optimization, Volume 59, Issue 3, Page 2273-2300, January 2021.
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.

中文翻译：

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古诺--动态环境中的纳什均衡和最优输运

SIAM Journal on Control and Optimization，第 59 卷，第 3 期，第 2273-2300 页，2021 年 1 月。
我们考虑离散时间的大型人口动态博弈。游戏的特点是玩家具有时间进化类型的特征，因此他们的行为不应该预测他们类型的未来价值。当玩家之间的交互是平均场类型时，我们将此类博弈的纳什均衡与动态古诺的渐近概念--纳什均衡联系起来。受 Blanchet 和 Carlier 对静态情况的著作的启发，我们根据因果最优传输理论解释了动态古诺-纳什均衡。进一步专门研究潜在类型的游戏，我们建立了均衡的存在性、唯一性和特征。此外，我们首次开发了因果最优传输的数值方案，然后利用该方案来计算动态古诺-纳什均衡。