2017/06/25 by Dmitry Khlopin, Khlopin, Dmitry
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Economic theories and models #Game Theory and Applications #Stochastic processes and financial applications #math.OC #msc:40E05 #msc:49L20 #msc:49N70 #msc:91A23 #msc:91A25
paper · pdf · doi:10.48550/arxiv.1706.08150
(in Russian)
arxiv created 2017/09/25 · arxiv updated 2017/09/26
This paper is concerned with two-person dynamic zero-sum games. Let games for some family have common dynamics, running costs and capabilities of players, and let these games differ in densities only. We show that the Dynamic Programming Principle directly leads to the General Tauberian Theorem---that the existence of a uniform limit of the value functions for uniform distribution or for exponential distribution implies that the value functions uniformly converge to the same limit for arbitrary distribution from large class. No assumptions on strategies are necessary. Applications to differential games and stochastic statement are considered.