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Title: Tauberian Theorem for Value Functions
Authors: Khlopin, D.
Issue Date: 2018
Publisher: Springer New York LLC
Citation: Khlopin D. Tauberian Theorem for Value Functions / D. Khlopin. — DOI 10.1007/s13235-017-0227-5 // Dynamic Games and Applications. — 2018. — Vol. 8. — Iss. 2. — P. 401-422.
Abstract: For two-person dynamic zero-sum games (both discrete and continuous settings), we investigate the limit of value functions of finite horizon games with long-run average cost as the time horizon tends to infinity and the limit of value functions of λ-discounted games as the discount tends to zero. We prove that the Dynamic Programming Principle for value functions directly leads to the Tauberian theorem—that the existence of a uniform limit of the value functions for one of the families implies that the other one also uniformly converges to the same limit. No assumptions on strategies are necessary. To this end, we consider a mapping that takes each payoff to the corresponding value function and preserves the sub- and superoptimality principles (the Dynamic Programming Principle). With their aid, we obtain certain inequalities on asymptotics of sub- and supersolutions, which lead to the Tauberian theorem. In particular, we consider the case of differential games without relying on the existence of the saddle point; a very simple stochastic game model is also considered. © 2017, Springer Science+Business Media, LLC.
Keywords: ABEL MEAN
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85036660808
PURE ID: 7144649
ISSN: 21530785
DOI: 10.1007/s13235-017-0227-5
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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