We study the stability of coalitions in multicriteria dynamic games. We use the Nash bargaining solution (Nash products) to construct a noncooperative equilibrium and the Nash bargaining solution for the entire planning horizon to find a cooperative solution. Conditions for the internal and external stability are extended to dynamic games with vector payoff functions. The notion of coalitional stability, which takes into account the stimuli for the player to transfer to other coalitions, is introduced. To illustrate the presented approach, we consider a multicriteria dynamic model of bioresource management. Conditions for the internal, external, and coalitional stability are presented.
Keywords: dynamic games, multicriteria games, Nash bargaining solution, internal and external stability, coalitional stability
Received July 30, 2019
Revised August 10, 2019
Accepted August 19, 2019
Funding Agency: This work was supported by the Shandong Province “Double-Hundred Talent Plan” (No. WST2017009).
Anna Nickolaevna Rettieva, Dr. Phys.-Math. Sci., School of Mathematics and Statistics, Qingdao University, Qingdao 266071, PR China; Institute of Applied Mathematics of Shandong, Qingdao 266071, PR China; Institute of Applied Mathematical Research of the Karelian Research Centre of the Russian Academy of Sciences, Petrozavodsk, 185910 Russia; e-mail: annaret@krc.karelia.ru
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Cite this article as: A.N. Rettieva. Coalitional stability conditions in multicriteria dynamic games, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 3, pp. 200–216.