In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under such strategies converges to zero in the large population size asymptotic. We show that these strategies satisfy an $Ł^\infty$ notion of approximate Nash equilibrium which guarantees that the individual gain from optimal unilateral deviation is small uniformly among players and uniformly on their initial characteristics. We establish these results in the context of static models and in the dynamic continuous time setting, and we cover situations where the agents' criteria depend on the conditional law of the controlled state process.

翻译：在大规模对称博弈的背景下，通过相应平均场博弈的均衡解引入了近似纳什均衡，其意义在于：在此类策略下，个体通过最优单边偏离所能获得的收益在大规模群体渐近条件下收敛于零。我们证明这些策略满足一种$L^\infty$意义上的近似纳什均衡概念，该概念保证个体通过最优单边偏离所能获得的收益在所有参与者间以及在其初始特征上均具有一致的小幅性。我们在静态模型与动态连续时间框架下建立了这些结果，并涵盖了智能体准则依赖于受控状态过程条件分布的情形。