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Subgame Consistent Solution For Cooperative Stochastic Dynamic Games With Random Horizon

Author

Listed:
  • 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)

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.

Suggested Citation

  • David W. K. Yeung & Leon A. Petrosyan, 2012. "Subgame Consistent Solution For Cooperative Stochastic Dynamic Games With Random Horizon," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 1-22.
    • Handle: RePEc:wsi:igtrxx:v:14:y:2012:i:02:n:s0219198912500120
    DOI: 10.1142/S0219198912500120
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    References listed on IDEAS

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    1. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    2. D. W. K. Yeung, 2008. "Dynamically Consistent Solution For A Pollution Management Game In Collaborative Abatement With Uncertain Future Payoffs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 517-538.
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    More about this item

    Keywords

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