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The Relationship between the Core and the Modified Cores of a Dynamic Game

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  • Artem Sedakov

    (Saint Petersburg State University, 7/9 Universitetskaya nab., 199034 Saint Petersburg, Russia
    School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
    Institute of Applied Mathematics of Shandong, Qingdao 266071, China)

  • Hao Sun

    (Saint Petersburg State University, 7/9 Universitetskaya nab., 199034 Saint Petersburg, Russia)

Abstract

The core as a solution to a cooperative game has the advantage that any imputation from it is undominated. In cooperative dynamic games, there is a known transformation that demonstrates another advantage of the core—time consistency—keeping players adhering to it during the course of the game. Such a transformation may change the solution, so it is essential that the new core share common imputations with the original one. In this paper, we will establish the relationship between the original core of a dynamic game and the core after the transformation, and demonstrate that the latter can be a subset of the former.

Suggested Citation

  • Artem Sedakov & Hao Sun, 2020. "The Relationship between the Core and the Modified Cores of a Dynamic Game," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1023-:d:375111
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    References listed on IDEAS

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    1. Parkash Chander & Henry Tulkens, 2006. "The Core of an Economy with Multilateral Environmental Externalities," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 153-175, Springer.
    2. Leon A Petrosyan & Nikolay A Zenkevich, 2016. "Game Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9824, January.
    3. Marc Germain & Philippe Toint & Henry Tulkens & Aart Zeeuw, 2006. "Transfers to Sustain Dynamic Core-Theoretic Cooperation in International Stock Pollutant Control," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 251-274, Springer.
    4. Heuvel, Wilco van den & Borm, Peter & Hamers, Herbert, 2007. "Economic lot-sizing games," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1117-1130, January.
    5. David W.K. Yeung & Leon A. Petrosyan, 2016. "Subgame Consistent Cooperation," Theory and Decision Library C, Springer, number 978-981-10-1545-8, March.
    6. Petrosyan, Leon & Sedakov, Artem & Sun, Hao & Xu, Genjiu, 2017. "Convergence of strong time-consistent payment schemes in dynamic games," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 96-112.
    7. Artem Sedakov, 2020. "Characteristic Function and Time Consistency for Two-Stage Games with Network Externalities," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    8. Drechsel, J. & Kimms, A., 2010. "Computing core allocations in cooperative games with an application to cooperative procurement," International Journal of Production Economics, Elsevier, vol. 128(1), pages 310-321, November.
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