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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2017, Volume 23, Number 1, Pages 219–227
DOI: https://doi.org/10.21538/0134-4889-2017-23-1-219-227
(Mi timm1397)
 

This article is cited in 3 scientific papers (total in 3 papers)

Construction of strongly time-consistent subcores in differential games with prescribed duration

L. A. Petrosyan, Ya. B. Pankratova

Saint Petersburg State University
Full-text PDF (170 kB) Citations (3)
References:
Abstract: A new strongly time-consistent (dynamically stable) optimality principle is proposed in a cooperative differential game. This is done by constructing a special subset of the core of the game. It is proposed to consider this subset as a new optimality principle. The construction is based on the introduction of a function $\hat{V}$ that dominates the values of the classical characteristic function in coalitions. Suppose that $V(S,\bar{x}(\tau),T-\tau)$ is the value of the classical characteristic function computed in the subgame with initial conditions $\bar{x}(\tau)$, $T-\tau$ on the cooperative trajectory. Define
$$\hat{V}(S;x_0,T-t_0)=\displaystyle\max_{t_0\leq \tau\leq T}\frac{V(S;x^*(\tau),T-\tau)}{V(N;x^*(\tau),T-\tau)}V(N;x_0,T-t_0).$$
Using this function, we construct an analog of the classical core. It is proved that the constructed core is a subset of the classical core; thus, we can consider it as a new optimality principle. It is proved also that the newly constructed optimality principle is strongly time-consistent.
Keywords: cooperative differential game, strong time consistency, core, subcore, imputation.
Received: 30.10.2016
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2018, Volume 301, Issue 1, Pages 137–144
DOI: https://doi.org/10.1134/S0081543818050115
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 37C75
Language: Russian
Citation: L. A. Petrosyan, Ya. B. Pankratova, “Construction of strongly time-consistent subcores in differential games with prescribed duration”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 1, 2017, 219–227; Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 137–144
Citation in format AMSBIB
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\by L.~A.~Petrosyan, Ya.~B.~Pankratova
\paper Construction of strongly time-consistent subcores in differential games with prescribed duration
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2017
\vol 23
\issue 1
\pages 219--227
\mathnet{http://mi.mathnet.ru/timm1397}
\crossref{https://doi.org/10.21538/0134-4889-2017-23-1-219-227}
\elib{https://elibrary.ru/item.asp?id=28409381}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2018
\vol 301
\issue , suppl. 1
\pages 137--144
\crossref{https://doi.org/10.1134/S0081543818050115}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000453520500020}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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