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Subgame Consistent Solution For Cooperative Stochastic Dynamic Games With Random Horizon

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  • DAVID W. K. YEUNG

    ()
    (SRS Consortium for Advanced Study in Cooperative Dynamic Games, Hong Kong Shue Yan University, Center of Game Theory, St Petersburg State University, St Petersburg, 198904, Russia)

  • LEON A. PETROSYAN

    ()
    (Faculty of Applied Mathematics-Control Processes, St Petersburg State University, St Petersburg, 198904, Russia)

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    Abstract

    In cooperative stochastic dynamic games a stringent condition — that of subgame consistency — is required for a dynamically stable cooperative solution. In particular, a cooperative solution is subgame consistent if an extension of the solution policy to a subgame starting at a later time with a state brought about by prior optimal behavior would remain optimal. This paper extends subgame consistent solutions to cooperative stochastic dynamic (discrete-time) games with random horizon. In the analysis new forms of the stochastic Bellman equation and the stochastic Isaacs–Bellman equation in discrete time are derived. Subgame consistent cooperative solutions are obtained for stochastic dynamic games. Analytically tractable payoff distribution mechanisms which lead to the realization of these solutions are developed. This is the first time that subgame consistent solutions for cooperative stochastic dynamic games with random horizon are presented.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

    Volume (Year): 14 (2012)
    Issue (Month): 02 ()
    Pages: 1250012-1-1250012-22

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    Handle: RePEc:wsi:igtrxx:v:14:y:2012:i:02:p:1250012-1-1250012-22

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    Related research

    Keywords: Stochastic dynamic games; Random horizon; Stochastic Bellman equation; Stochastic Hamilton–Jacobi–Bellman equation;

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