Bayesian equilibrium: From local to global
研究了状态空间连续且分成多个共同知识部分的贝叶斯博弈，证明了在一定的正则条件下，整体上存在可测的贝叶斯均衡，并扩展到纯策略均衡、非紧行动集等多种情形。
We study Bayesian games with a continuum of states which partition into a continuum of components, each of which is common knowledge, such that equilibria exist on each component. A canonical case is when each agent’s information consists of both public and private information, and conditional on each possible public signal, equilibria exist. We show that under some regularity conditions on the partition, measurable Bayesian equilibria exist for the game in its entirety. The results extend to pure equilibria, as well as to non-compact state-dependent action sets, uncommon priors, and non-bounded payoffs; the results also apply to several notions of approximate equilibria.