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 Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 3, Pages 193–203 (Mi timm1094)

Two-level cooperation in coalitional differential games

L. A. Petrosyan, E. V. Gromova

Saint Petersburg State University

Abstract: We consider a differential game with prescribed duration and given coalitional partition of the set of players. The cooperative game proceeds in two stages. At the first stage the players (coalitions) maximize the total payoff and then distribute it according to the Shapley value. At the second stage the components of the Shapley value are distributed inside fixed coalitions. We study the time consistency of the proposed two-level cooperative solution. The problem is solved by means of an imputation distribution procedure. The results are illustrated by a differential game of emission reduction.

Keywords: cooperative differential games, Shapley value, imputation distribution procedure, time consistency.

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UDC: 519.83

Citation: L. A. Petrosyan, E. V. Gromova, “Two-level cooperation in coalitional differential games”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 3, 2014, 193–203

Citation in format AMSBIB
\Bibitem{PetGro14} \by L.~A.~Petrosyan, E.~V.~Gromova \paper Two-level cooperation in coalitional differential games \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2014 \vol 20 \issue 3 \pages 193--203 \mathnet{http://mi.mathnet.ru/timm1094} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3379224} \elib{https://elibrary.ru/item.asp?id=23503121} 

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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. Nikolai V. Kolabutin, “Dvukhurovnevaya kooperatsiya v differentsialnoi igre sokrascheniya vrednykh vybrosov”, MTIP, 6:4 (2014), 3–36
2. E. V. Gromova, L. A. Petrosyan, “Silno dinamicheski ustoichivoe kooperativnoe reshenie v odnoi differentsialnoi igre upravleniya vrednymi vybrosami”, UBS, 55 (2015), 140–159
3. Ekaterina Gromova, Kristina Plekhanova, “A differential game of pollution control with participation of developed and developing countries”, Contributions to Game Theory and Management, 8 (2015), 64–83
4. Ekaterina V. Gromova, Leon A. Petrosyan, “On a approach to the construction of characteristic function for cooperative differential games”, Autom. Remote Control, 78:9 (2017), 1680–1692
5. Ekaterina V. Gromova, Ekaterina V. Marova, “On the characteristic function construction technique in differential games with prescribed and random duration”, Contributions to Game Theory and Management, 11 (2018), 53–65
6. E. V. Gromova, E. V. Marova, “Coalition and anti-coalition interaction in cooperative differential games”, IFAC-PapersOnLine, 51:32 (2018), 479–483
7. L. Petrosyan, D. W. K. Yeung, “The two level cooperation in a class of $n$-person differential games”, IFAC-PapersOnLine, 51:32 (2018), 585–587
8. L. A. Petrosyan, D. V. K. Yang, “Dvukhurovnevaya kooperatsiya v odnom klasse neantagonisticheskikh differentsialnykh igr”, Tr. IMM UrO RAN, 25, no. 1, 2019, 166–173
9. Ekaterina V. Gromova, Igor I. Evlampiev, “Coalition power estimation. Overview from the mathematical and philosophical perspectives”, Contributions to Game Theory and Management, 13 (2020), 142–151
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