TY - JOUR AU - Page, Frank H. AU - Fu, Jing PY - 2020 DA - 2020/09/22 TI - K-Correspondences, USCOs, and fixed point problems arising in discounted stochastic games JO - Fixed Point Theory and Applications SP - 14 VL - 2020 IS - 1 AB - We establish a fixed point theorem for the composition of nonconvex, measurable selection valued correspondences with Banach space valued selections. We show that if the underlying probability space of states is nonatomic and if the selection correspondences in the composition are K-correspondences (meaning correspondences having graphs that contain their Komlos limits), then the induced measurable selection valued composition correspondence takes contractible values and therefore has fixed points. As an application we use our fixed point result to show that all nonatomic uncountable-compact discounted stochastic games have stationary Markov perfect equilibria – thus resolving a long-standing open question in game theory. SN - 1687-1812 UR - https://doi.org/10.1186/s13663-020-00681-1 DO - 10.1186/s13663-020-00681-1 ID - Page2020 ER -