论文标题
在动态环境中
Cournot-Nash equilibrium and optimal transport in a dynamic setting
论文作者
论文摘要
我们考虑在离散时间内进行大量人口动态游戏。游戏的特殊性是玩家的特征是随着时间的推移类型，因此他们的行动不应预见其类型的未来价值。当玩家之间的互动是均值的场合时，我们将纳什的均衡与此类游戏相关联与动态的cournot-nash平衡的渐近概念相关联。受Blanchet和Carlier在静态情况下的作品的启发，我们根据因果最佳运输理论来解释动态的Cournot-Nash平衡。进一步专门研究潜在类型的游戏，我们建立了平衡的存在，独特性和特征。此外，我们首次开发了一种用于因果最佳运输的数值方案，然后利用该方案来计算动态的cournot-nash平衡。在交通拥堵游戏的详细案例研究中说明了这一点。
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.
