document: The semi-algebraic theory of stochastic games The asymptotic behavior of the min-max value of a finite-state zero-sum discounted stochastic game , as the discount rate approaches 0 , has been studied in the past using the theory of real-closed fields . We use the theory of semi-algebraic sets and mappings to prove some asymptotic properties of the min-max value , which hold uniformly for all stochastic games in which the number of states and players ' actions are predetermined to some fixed values . As a corollary , we prove a uniform polynomial convergence rate of the value of the N-stage game to the value of the nondiscount game , over a bounded set of payoffs
doc_bio_tags: O O O O O O O B I O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: asymptotic behavior discount rate uniform polynomial convergence rate
abstractive_keyphrases: finite-state zero-sum discounted stochastic game semi-algebraic set theory min-max value n-stage game two-player zero-sum finite-state stochastic games