We introduce and investigate certain N player dynamic games on the line and in the plane that admit Coulomb gas dynamics as a Nash equilibrium. Most significantly, we find that the universal local limit of the equilibrium is sensitive to the chosen model of player information in one dimension but not in two dimensions. We also find that players can achieve game theoretic symmetry through selfish behavior despite non-exchangeability of states, which allows us to establish strong localized convergence of the N-Nash systems to the expected mean field equations when tested against locally optimal player ensembles, i.e., against those exhibiting the same local limit as the Nash-optimal ensemble. In one dimension, this convergence notably features a nonlocal-to-local transition in the population dependence of the N-Nash system.

中文翻译：

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戴森和库仑游戏

我们在直线上和平面上引入和研究某些N玩家动态游戏，这些游戏将库仑气体动力学视为纳什均衡。最重要的是，我们发现均衡的通用局部极限在一个维度上对所选玩家信息模型敏感，而在两个维度上则不敏感。我们还发现，尽管状态不可交换，但玩家仍可以通过自私的行为实现游戏理论对称性，这使我们能够建立N的强大局部收敛性-针对局部最优播放器集合（即，与Nash最优集合具有相同局部极限的系统）进行测试时，将Nash系统转换为预期的平均场方程。在一个维度上，这种收敛在N -Nash系统的人口依赖性方面具有非局部到局部的过渡。