We consider multi-population Bayesian games with a large number of players. Each player aims at minimizing a cost function that depends on her own action, the distribution of players' actions in all populations, and an unknown state parameter. We study the nonatomic limit versions of these games. We 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, are reduced to 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 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：我们考虑具有大量参与者的多群体贝叶斯博弈。每个参与者的目标是最小化一个依赖于自身行动、所有群体中参与者行动的分布以及未知状态参数的代价函数。我们研究了这些博弈的非原子极限版本，引入贝叶斯相关沃德罗普均衡概念，该概念将贝叶斯相关均衡扩展至非原子博弈。我们证明，贝叶斯相关沃德罗普均衡是由有限小参与者博弈的贝叶斯相关均衡诱导的行动流的极限。对于具有凸势函数的完全信息非原子博弈，我们证明相关均衡与粗相关沃德罗普均衡的集合简化为沃德罗普均衡的概率分布集合，且所有均衡结果具有相同代价。由此得到以下结论：第一，在具有有限参与者的凸势博弈中，（粗）相关均衡的所有流分布当每个参与者权重趋于零时收敛至沃德罗普均衡；第二，对于满足无遗憾性质的任意流序列，其经验分布收敛至沃德罗普均衡的分布集合，且平均代价收敛至唯一的沃德罗普代价。