The Asymptotic Value in Finite Stochastic Games
成果类型：
Article
署名作者：
Oliu-Barton, Miquel
署名单位：
Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2013.0642
发表日期：
2014
页码：
712-721
关键词：
摘要：
Bewley and Kohlberg [Bewley T, Kohlberg E (1976) The asymptotic theory of stochastic games. Math. Oper. Res. 1: 197-208] proved that the discounted values of finite zero-sum stochastic games have a limit, as the discount factor tends to zero, using the Tarski-Seidenberg elimination theorem from real algebraic geometry. This was a fundamental step in the development of the theory of stochastic games. The current paper provides a new and direct proof for this result, relying on the explicit description of asymptotically optimal strategies. Moreover, we prove that our approach can also be used to obtain the existence of the uniform value, as in Mertens and Neyman [Mertens J-F, Neyman A (1981) Stochastic games.