Abstract
We study the stability of coalitions in multicriteria dynamic games. We use the bargaining construction (Nash product) to obtain a noncooperative equilibrium and the Nash bargaining scheme for the entire duration of the game 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 players 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.
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References
L. S. Shapley and F. D. Rigby, “Equilibrium points in games with vector payoffs,” Naval Res. Logist. Quart. 6 (1), 57–61 (1959). doi https://doi.org/10.1002/nav.3800060107
M. Voorneveld, S. Grahn, and M. Dufwenberg, “Ideal equilibria in noncooperative multicriteria games,” Math. Methods Oper. Res. 52 (1), 65–77 (2000). doi https://doi.org/10.1007/s001860000069
L. Pusillo and S. Tijs, “E-equilibria for multicriteria games,” in Advances in Dynamic Games: Theory, Applications, and Numerical Methods for Differential and Stochastic Games (Birkhäuser, Boston, 2013), Ser. Annals of the International Society of Dynamic Games 12, pp. 217–228.
A. N. Rettieva, “Equilibria in Dynamic Multicriteria Games,” Internat. Game Theory Rev. 19 (1), paper 1750002 (2017). doi 10.1142/S0219198917500025
A. N. Rettieva, “Dynamic multicriteria games with finite horizon,” Mathematics 6 (9), paper 156 (2018). doi 10.3390/math6090156
A. N. Rettieva, “Coalition formation in dynamic multicriteria games,” Autom. Remote Control 80 (10), 345–357 (2019). doi https://doi.org/10.1134/S0005117919100114
C. D’Aspremont, A. Jacquemin, J. J. Gabszewicz, and J. A. Weymark, “On the stability of collusive price leadership” Canad. J. Econ. 16 (1), 17–25 (1983). doi https://doi.org/10.2307/134972
C. Carraro, “The structure of international environmental agreements,” in International Environmental Agreements on Climate Change (Springer, Dordrecht, 1999) pp. 9–25.
A. Rettieva, “Coalition stability in dynamic multicriteria games,” in Mathematical Optimization Theory and Operations Research: Proceedings of the 18th International Conference, Yekaterinburg, Russia, 2019 (Springer, Cham, 2019), Ser. Lecture Notes in Computer Science 11548, pp. 697–714.
A. N. Rettieva, “Stable coalition structure in bioresource management problem,” Ecol. Model. 235, 102–118 (2012). doi https://doi.org/10.1016/j.ecolmodel.2012.03.015
A. de Zeeuw, “Dynamic effects on stability of international environmental agreements,” J. Environ. Econ. Management 55 (2), 163–174 (2008). doi https://doi.org/10.1016/j.jeem.2007.06.003
Funding
This work was supported by the Shandong province “Double-Hundred Talent Plan” (no. WST2017009).
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Rettieva, A.N. Coalitional Stability Conditions in Multicriteria Dynamic Games. Proc. Steklov Inst. Math. 307 (Suppl 1), 99–115 (2019). https://doi.org/10.1134/S0081543819070083
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DOI: https://doi.org/10.1134/S0081543819070083