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IDP-Core: Novel Cooperative Solution for Differential Games

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  • Ovanes Petrosian

    (College of Mathematics and Computer Science, Yanan University, Yan’an 716000, China
    Faculty of Applied Mathematics and Control Processes, St. Petersburg University, Universitetskaya naberezhnaya 7-9, 199034 St. Petersburg, Russia)

  • Victor Zakharov

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg University, Universitetskaya naberezhnaya 7-9, 199034 St. Petersburg, Russia)

Abstract

IDP-core is a new cooperative solution for dynamic and differential games. A novel approach of constructing solutions for dynamic and differential games was employed in which the time consistency property was used as the main axiom property for the cooperative solution. Another new and important approach used for constructing IDP-core is the IDP dominance, which allows to select undominated imputation distribution procedures and construct the cooperative solution or imputation set. This approach shows the potential of using the time consistency property as the main axiom for solutions in various fields such as Social Choice and Mechanism Design. The overall procedure for defining the cooperative solution is also new since IDP-core was constructed using imputation distribution procedures but not by using imputations directly.

Suggested Citation

  • Ovanes Petrosian & Victor Zakharov, 2020. "IDP-Core: Novel Cooperative Solution for Differential Games," Mathematics, MDPI, vol. 8(5), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:721-:d:353819
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    References listed on IDEAS

    as
    1. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    2. Victor Zakharov & Maria Dementieva, 2004. "Multistage Cooperative Games And Problem Of Time Consistency," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 157-170.
    3. 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.
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