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Equilibria in Dynamic Multicriteria Games

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  • Anna Rettieva

    (Institute of Applied Mathematical Research, Karelian Research Centre of RAS, Pushkinskaya str., 11, Petrozavodsk 185910, Russia)

Abstract

Mathematical models involving more than one objective seem more adherent to real problems. Often players have more than one goal which are often not comparable. These situations are typical for game-theoretic models in economic and ecology. In this paper, new approaches to construct equilibria in dynamic multicriteria games are constructed. We consider a dynamic, discrete-time, game model where the players use a common resource and have different criteria to optimize. First, we construct the guaranteed payoffs in a several ways. Then, we find an equilibrium as a solution of a Nash bargaining scheme with the guaranteed payoffs playing the role of status quo points. The obtained equilibrium, called a multicriteria Nash equilibrium, gives a possible solution concept for dynamic multicriteria games.

Suggested Citation

  • Anna Rettieva, 2017. "Equilibria in Dynamic Multicriteria Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-21, March.
    • Handle: RePEc:wsi:igtrxx:v:19:y:2017:i:01:n:s0219198917500025
    DOI: 10.1142/S0219198917500025
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    References listed on IDEAS

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    1. Mark Voorneveld & Sofia Grahn & Martin Dufwenberg, 2000. "Ideal equilibria in noncooperative multicriteria games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 65-77, September.
    2. Fioravante Patrone & Lucia Pusillo & Stef Tijs, 2007. "Multicriteria games and potentials," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 138-145, July.
    3. Patrone, F. & Pusillo, L. & Tijs, S.H., 2007. "Multicriteria games and potentials," Other publications TiSEM 47a4248e-bbe4-4037-99f1-f, Tilburg University, School of Economics and Management.
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    Citations

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    Cited by:

    1. Anna Rettieva, 2018. "Dynamic Multicriteria Games with Finite Horizon," Mathematics, MDPI, vol. 6(9), pages 1-9, September.
    2. Bertrand Crettez & Naila Hayek & Peter M. Kort, 2021. "A Dynamic Multi-Objective Duopoly Game with Capital Accumulation and Pollution," Mathematics, MDPI, vol. 9(16), pages 1-34, August.
    3. Anna N. Rettieva, 2022. "Dynamic multicriteria games with asymmetric players," Journal of Global Optimization, Springer, vol. 83(3), pages 521-537, July.
    4. Sasaki, Yasuo, 2022. "Unawareness of decision criteria in multicriteria games," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 31-40.
    5. Anna Rettieva, 2022. "Dynamic Multicriteria Game with Pollution Externalities," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    6. Anna Rettieva, 2020. "Rational Behavior in Dynamic Multicriteria Games," Mathematics, MDPI, vol. 8(9), pages 1-16, September.
    7. Anna N. Rettieva, 2020. "Cooperation in dynamic multicriteria games with random horizons," Journal of Global Optimization, Springer, vol. 76(3), pages 455-470, March.
    8. Jaeok Park, 2019. "Decision Making and Games with Vector Outcomes," Working papers 2019rwp-146, Yonsei University, Yonsei Economics Research Institute.

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