Measurable Selection for Purely Atomic Games
提出一个可测选择定理，在状态空间可分解为可数等价类的条件下，构造从状态空间到参数空间的可测映射，并证明该定理可用于证明多种博弈（如贝叶斯博弈、随机博弈、图博弈）中可测均衡的存在性。
A general selection theorem is presented constructing a measurable mapping from a state space to a parameter space under the assumption that the state space can be decomposed as a collection of countable equivalence classes under a smooth equivalence relation. It is then shown how this selection theorem can be used as a general purpose tool for proving the existence of measurable equilibria in broad classes of several branches of games when an appropriate smoothness condition holds, including Bayesian games with atomic knowledge spaces, stochastic games with countable orbits, and graphical games of countable degree—examples of a subclass of games with uncountable state spaces that we term purely atomic games. Applications to repeated games with symmetric incomplete information and acceptable bets are also presented.