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Multistage Cooperative Games And Problem Of Time Consistency

Author

Listed:
  • VICTOR ZAKHAROV

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, Bibliotechnaya pl. 2., St. Petersburg, 198504, Russia)

  • MARIA DEMENTIEVA

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, Bibliotechnaya pl. 2., St. Petersburg, 198504, Russia)

Abstract

In this paper we consider the problem of time-consistency of the subcore in a multistage TU-cooperative game. We propose necessary and sufficient conditions for the time-consistency of an imputation from the subcore. Based on these conditions, we suggest an algorithm providing time-consistency of a selector of the subcore. Besides, we prove consistency of the subcore with respect to the MDM-reduction. Finally we introduce the notions of reduced game and dynamic consistency for multistage cooperative games. One of the main results of this paper is a theorem stating some properties of dynamic consistency of the subcore selectors. We focus particularly on the conditions of the dynamic consistency of the subcore with respect to the MDM-reduced game.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:igtrxx:v:06:y:2004:i:01:n:s0219198904000125
    DOI: 10.1142/S0219198904000125
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    Citations

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    Cited by:

    1. Calleja, Pedro & Rafels, Carles & Tijs, Stef, 2009. "The aggregate-monotonic core," Games and Economic Behavior, Elsevier, vol. 66(2), pages 742-748, July.
    2. Denis Kuzyutin & Nadezhda Smirnova, 2020. "Subgame Consistent Cooperative Behavior in an Extensive form Game with Chance Moves," Mathematics, MDPI, vol. 8(7), pages 1-20, July.
    3. Ovanes Petrosian & Victor Zakharov, 2020. "IDP-Core: Novel Cooperative Solution for Differential Games," Mathematics, MDPI, vol. 8(5), pages 1-20, May.

    More about this item

    Keywords

    Multistage TU-cooperative games; core; subcore; time-consistency; dynamic consistency; reduced game;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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