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Rational Behavior in Dynamic Multicriteria Games

Author

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  • Anna Rettieva

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
    Institute of Applied Mathematics of Shandong, Qingdao 266071, China
    Institute of Applied Mathematical Research Karelian Research Center of RAS, 11, Pushkinskaya str., Petrozavodsk 185910, Russia
    Saint Petersburg State University, 7/9, Universitetskaya nab., Saint Petersburg 199034, Russia)

Abstract

We consider a dynamic, discrete-time, game model where n players use a common resource and have different criteria to optimize. To construct a multicriteria Nash equilibrium the bargaining solution is adopted. To design a multicriteria cooperative equilibrium, a modified bargaining scheme that guarantees the fulfillment of rationality conditions is applied. The concept of dynamic stability is adopted for dynamic multicriteria games. To stabilize the multicriteria cooperative solution a time-consistent payoff distribution procedure is constructed. The conditions for rational behavior, namely irrational-behavior-proofness condition and each step rational behavior condition are defined for dynamic multicriteria games. To illustrate the presented approaches, a dynamic bi-criteria bioresource management problem with many players is investigated.

Suggested Citation

  • Anna Rettieva, 2020. "Rational Behavior in Dynamic Multicriteria Games," Mathematics, MDPI, vol. 8(9), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1485-:d:407879
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    References listed on IDEAS

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    1. Leon A Petrosyan & Nikolay A Zenkevich, 2016. "Game Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9824, September.
    2. Anna Rettieva, 2018. "Dynamic Multicriteria Games with Finite Horizon," Mathematics, MDPI, vol. 6(9), pages 1-9, September.
    3. Anna N. Rettieva, 2020. "Cooperation in dynamic multicriteria games with random horizons," Journal of Global Optimization, Springer, vol. 76(3), pages 455-470, March.
    4. Petrosjan, Leon & Zaccour, Georges, 2003. "Time-consistent Shapley value allocation of pollution cost reduction," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 381-398, January.
    5. Parkash Chander, 2007. "The gamma-core and coalition formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 539-556, April.
    6. 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.
    7. Rettieva, Anna N., 2017. "Cooperation in Bioresource Management Problems," Conference Papers 10464, Graduate School of Management, St. Petersburg State University.
    8. Mazalov, V.V. & Rettieva, A.N., 2010. "Fish wars and cooperation maintenance," Ecological Modelling, Elsevier, vol. 221(12), pages 1545-1553.
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    Cited by:

    1. Anna Rettieva, 2022. "Dynamic Multicriteria Game with Pollution Externalities," Mathematics, MDPI, vol. 10(22), pages 1-15, November.

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