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Sustainable Cooperation in Dynamic Games on Event Trees with Players’ Asymmetric Beliefs

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  • Elena M. Parilina

    (Saint Petersburg State University
    Qingdao University)

  • Georges Zaccour

    (GERAD, HEC Montréal)

Abstract

We built a time-consistent cooperative solution for the class of dynamic games played over event trees in the context where the tree structure is given, but the players have different beliefs about the transition probabilities between nodes. Our three-step approach is as follows. First, we consider three alternative methods for aggregating the players’ beliefs and assume that the players agree to adopt one of them if they decide to cooperate. Second, we determine the Nash bargaining outcomes for the whole duration of the game. Finally, to insure sustainability of cooperation throughout the whole duration of the game, we propose two time-consistent decompositions over nodes of each player’s cooperative share, namely a proportion-consistent and a node-consistent allocation schemes. We illustrate our results with a simple Cournot oligopoly with capacity constraints.

Suggested Citation

  • Elena M. Parilina & Georges Zaccour, 2022. "Sustainable Cooperation in Dynamic Games on Event Trees with Players’ Asymmetric Beliefs," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 92-120, July.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:1:d:10.1007_s10957-022-02010-5
    DOI: 10.1007/s10957-022-02010-5
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    References listed on IDEAS

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    1. Elena Parilina & Georges Zaccour, 2016. "Strategic Support of Node-Consistent Cooperative Outcomes in Dynamic Games Played Over Event Trees," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-16, June.
    2. Ouchi, Fumika, 2004. "A literature review on the use of expert opinion in probabilistic risk analysis," Policy Research Working Paper Series 3201, The World Bank.
    3. Dietrich, Franz & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
    4. Alain Haurie & Jacek B Krawczyk & Georges Zaccour, 2012. "Games and Dynamic Games," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8442, February.
    5. Elena M. Parilina & Alessandro Tampieri, 2018. "Stability and cooperative solution in stochastic games," Theory and Decision, Springer, vol. 84(4), pages 601-625, June.
    6. Franz Dietrich, 2010. "Bayesian group belief," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 595-626, October.
    7. Elena M. Parilina & Georges Zaccour, 2017. "Node-Consistent Shapley Value for Games Played over Event Trees with Random Terminal Time," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 236-254, October.
    8. Genc, Talat S. & Sen, Suvrajeet, 2008. "An analysis of capacity and price trajectories for the Ontario electricity market using dynamic Nash equilibrium under uncertainty," Energy Economics, Elsevier, vol. 30(1), pages 173-191, January.
    9. Pineau, Pierre-Olivier & Rasata, Hasina & Zaccour, Georges, 2011. "Impact of some parameters on investments in oligopolistic electricity markets," European Journal of Operational Research, Elsevier, vol. 213(1), pages 180-195, August.
    10. Xiaomin You & Fulvio Tonon, 2012. "Event‐Tree Analysis with Imprecise Probabilities," Risk Analysis, John Wiley & Sons, vol. 32(2), pages 330-344, February.
    11. Genc, Talat S. & Reynolds, Stanley S. & Sen, Suvrajeet, 2007. "Dynamic oligopolistic games under uncertainty: A stochastic programming approach," Journal of Economic Dynamics and Control, Elsevier, vol. 31(1), pages 55-80, January.
    12. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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    Cited by:

    1. Parilina, Elena M. & Zaccour, Georges, 2024. "Payment schemes for sustaining cooperation in dynamic games played over event trees," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1200-1216.

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