We consider multi-population Bayesian games with a large number of players. Each player aims at minimizing a cost function that depends on this player's own action, the distribution of players' actions in all populations, and an unknown state parameter. We study the nonatomic limit versions of these games and introduce the concept of Bayes correlated Wardrop equilibrium, which extends the concept of Bayes correlated equilibrium to nonatomic games. We prove that Bayes correlated Wardrop equilibria are limits of action flows induced by Bayes correlated equilibria of the game with a large finite set of small players. For nonatomic games with complete information admitting a convex potential, we prove that the set of correlated and of coarse correlated Wardrop equilibria coincide with the set of probability distributions over Wardrop equilibria, and that all equilibrium outcomes have the same costs. We get the following consequences. First, all flow distributions of (coarse) correlated equilibria in convex potential games with finitely many players converge to Wardrop equilibria when the weight of each player tends to zero. Second, for any sequence of flows satisfying a no-regret property, its empirical distribution converges to the set of distributions over Wardrop equilibria and the average cost converges to the unique Wardrop cost.

翻译：我们考虑具有大量玩家的多群体贝叶斯博弈。每个玩家的目标是最小化一个依赖于自身行动、所有群体中玩家行动的分布以及未知状态参数的代价函数。我们研究这些博弈的非原子极限版本，并引入贝叶斯关联沃德罗普均衡的概念，该概念将贝叶斯关联均衡扩展至非原子博弈。我们证明，贝叶斯关联沃德罗普均衡是由大量小玩家组成的有限博弈中关联均衡所诱导的行动流的极限。对于具有完全信息且存在凸势函数的非原子博弈，我们证明关联均衡与粗关联沃德罗普均衡的集合与沃德罗普均衡上的概率分布集合重合，且所有均衡结果具有相同的代价。我们得到以下结论：首先，在具有有限玩家的凸势博弈中，当每个玩家的权重趋于零时，（粗）关联均衡的所有流分布收敛至沃德罗普均衡。其次，对于任意满足无遗憾性质的流序列，其经验分布收敛至沃德罗普均衡上的分布集，且平均代价收敛至唯一的沃德罗普代价。