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Sbornik: Mathematics, 2018, Volume 209, Issue 1, Pages 122–144
DOI: https://doi.org/10.1070/SM8785 (Mi sm8785) 		 
This article is cited in 5 scientific papers (total in 5 papers)

A uniform Tauberian theorem in dynamic games

D. V. Khlopin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
English version PDF (601 kB) Citations (5)
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DOI: https://doi.org/10.1070/SM8785
Abstract: Antagonistic dynamic games including games represented in normal form are considered. The asymptotic behaviour of value in these games is investigated as the game horizon tends to infinity (Cesàro mean) and as the discounting parameter tends to zero (Abel mean). The corresponding Abelian-Tauberian theorem is established: it is demonstrated that in both families the game value uniformly converges to the same limit, provided that at least one of the limits exists. Analogues of one-sided Tauberian theorems are obtained. An example shows that the requirements are essential even for control problems.
Bibliography: 31 titles.
Keywords: dynamic programming principle, games with a saddle point, Tauberian theorem.
Received: 14.07.2016 and 17.02.2017
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 1, Pages 127–150
DOI: https://doi.org/10.4213/sm8785
Bibliographic databases:
Document Type: Article
UDC: 519.837.4+517.521.75
MSC: 40E05, 91A25
Language: English
Original paper language: Russian
Citation: D. V. Khlopin, “A uniform Tauberian theorem in dynamic games”, Mat. Sb., 209:1 (2018), 127–150; Sb. Math., 209:1 (2018), 122–144
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:70
    First page:23
     
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