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
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.
dynamic programming principle, games with a saddle point, Tauberian theorem.
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Sbornik: Mathematics, 2018, 209:1, 122–144
MSC: 40E05, 91A25
Received: 14.07.2016 and 17.02.2017
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
\paper A~uniform Tauberian theorem in dynamic games
\jour Mat. Sb.
\jour Sb. Math.
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This publication is cited in the following articles:
D. Khlopin, “Tauberian theorem for value functions”, Dyn. Games Appl., 8:2 (2018), 401–422
D. V. Khlopin, “Value asymptotics in dynamic games on large horizons”, St. Petersburg Math. J., 31:1 (2020), 157–179
D. V. Khlopin, “On Tauberian theorem for stationary Nash equilibria”, Optim. Lett., 13:8 (2019), 1855–1870
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
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