Continuity Properties of Value Functions in Information Structures for Zero-Sum and General Games and Stochastic Teams

We study continuity properties of stochastic game problems with respect to various topologies on information structures, defined as probability measures characterizing a game. will establish the value function under total variation, setwise, and weak convergence structures. Our analysis reveals that for bounded is continuous variation structures in both zero-sum games team problems. Continuity may fail hold setwise or structures; however, exhibits upper semicontinuity problems, lower when such through Blackwell-garbled sequence If individual channels are independent, fixed, satisfy condition, then functions priors. finally show players not be even general non-zero-sum games.