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Mat. Sb., 2018, Volume 209, Number 1, Pages 127–150 (Mi msb8785)  

This article is cited in 4 scientific papers (total in 4 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

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.

DOI: https://doi.org/10.4213/sm8785

Full text: PDF file (612 kB)
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English version:
Sbornik: Mathematics, 2018, 209:1, 122–144

Bibliographic databases:

UDC: 519.837.4+517.521.75
MSC: 40E05, 91A25
Received: 14.07.2016 and 17.02.2017

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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  • https://doi.org/10.4213/sm8785
  • http://mi.mathnet.ru/eng/msb/v209/i1/p127

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. Khlopin, “Tauberian theorem for value functions”, Dyn. Games Appl., 8:2 (2018), 401–422  crossref  mathscinet  zmath  isi  scopus
    2. D. V. Khlopin, “Value asymptotics in dynamic games on large horizons”, St. Petersburg Math. J., 31:1 (2020), 157–179  mathnet  crossref  isi  elib
    3. D. V. Khlopin, “On Tauberian theorem for stationary Nash equilibria”, Optim. Lett., 13:8 (2019), 1855–1870  crossref  mathscinet  zmath  isi  scopus
    4. D. Khlopin, “General limit value for stationary Nash equilibrium”, Mathematical optimization theory and operations research. 18th international conference, MOTOR 2019 (Ekaterinburg, Russia, July 8–12, 2019), Lecture Notes in Computer Science, 11548, eds. Khachay M., Kochetov Y., Pardalos P., Springer, Cham, 2019, 607–619  crossref  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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