2016/09/07 by Bruno Ziliotto, Ziliotto, Bruno
Economics, Econometrics and Finance · Mathematics · #47N10 #91A05 #91A15 #91A20 #91A25 #Economic theories and models #FOS: Mathematics #Game Theory and Voting Systems #Optimization and Control (math.OC) #Stochastic processes and financial applications #math.OC #msc:47N10 #msc:91A05 #msc:91A15 #msc:91A20 #msc:91A25
paper · pdf · doi:10.48550/arxiv.1609.02175
arxiv created 2016/09/07 · openalex publication_date 2016/09/07 · arxiv updated 2016/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proves several Tauberian theorems for general iterations of operators, and provides two applications to zero-sum stochastic games where the total payoff is a weighted sum of the stage payoffs. The first application is to provide conditions under which the existence of the asymptotic value implies the convergence of the values of the weighted game, as players get more and more patient. The second application concerns stochastic games with finite state space and action sets. This paper builds a simple class of asymptotically optimal strategies in the weighted game, that at each stage play optimally in a discounted game with a discount factor corresponding to the relative weight of the current stage.