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Strong Time-Consistent Solution for Cooperative Differential Games with Network Structure

Author

Listed:
  • Anna Tur

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia)

  • Leon Petrosyan

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia)

Abstract

One class of cooperative differential games on networks is considered. It is assumed that interaction on the network is possible not only between neighboring players, but also between players connected by paths. Various cooperative optimality principles and their properties for such games are investigated. The construction of the characteristic function is proposed, taking into account the network structure of the game and the ability of players to cut off connections. The conditions under which a strong time-consistent subcore is not empty are studied. The formula for explicit calculation of the Shapley value is derived. The results are illustrated by the example of one differential marketing game.

Suggested Citation

  • Anna Tur & Leon Petrosyan, 2021. "Strong Time-Consistent Solution for Cooperative Differential Games with Network Structure," Mathematics, MDPI, vol. 9(7), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:755-:d:528128
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    References listed on IDEAS

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    5. Leon A. Petrosjan & Nikolay A. Zenkevich, 1996. "Differential games," World Scientific Book Chapters, in: Game Theory, chapter 5, pages 267-343, World Scientific Publishing Co. Pte. Ltd..
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    8. Gao, Hongwei & Pankratova, Yaroslavna, 2017. "Cooperation in Dynamic Network Games," Conference Papers 10451, Graduate School of Management, St. Petersburg State University.
    9. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. David W.K. Yeung & Leon A. Petrosyan, 2016. "Subgame Consistent Cooperation," Theory and Decision Library C, Springer, number 978-981-10-1545-8, December.
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