Bayesian games with a continuum of states
研究了当共同知识关系平滑时，纯原子类型的贝叶斯博弈存在可测均衡；反之，若关系不平滑，则存在无均衡的博弈，并排除了两种悖论。
We show that every Bayesian game with purely atomic \ntypes has a measurable Bayesian equilibrium when the common knowl- \nedge relation is smooth. Conversely, for any common knowledge rela- \ntion that is not smooth, there exists a type space that yields this common \nknowledge relation and payoffs such that the resulting Bayesian game \nwill not have any Bayesian equilibrium. We show that our smoothness \ncondition also rules out two paradoxes involving Bayesian games with \na continuum of types: the impossibility of having a common prior on \ncomponents when a common prior over the entire state space exists, and \nthe possibility of interim betting/trade even when no such trade can be \nsupported \nex ante.