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Subgame Consistent Solutions for Cooperative Stochastic Dynamic Games

Author

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  • D. W. K. Yeung

    (Hong Kong Shue Yan University
    St. Petersburg State University)

  • L. A. Petrosyan

    (St. Petersburg State University
    St. Petersburg State University)

Abstract

In cooperative games over time with uncertainty, a stringent condition (subgame consistency) is required for a dynamically stable solution. In particular, a cooperative solution is subgame consistent if an extension of the solution policy to a situation with a later starting time and any feasible state brought about by prior optimal behavior would remain optimal. This paper derives an analytically tractable payoff distribution procedure leading to the realization of subgame consistent solutions in cooperative stochastic dynamic games. This is the first time that subgame consistent solutions in discrete-time dynamic games under uncertainty are provided.

Suggested Citation

  • D. W. K. Yeung & L. A. Petrosyan, 2010. "Subgame Consistent Solutions for Cooperative Stochastic Dynamic Games," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 579-596, June.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:3:d:10.1007_s10957-010-9702-5
    DOI: 10.1007/s10957-010-9702-5
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    References listed on IDEAS

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    1. D.W.K. Yeung & L.A. Petrosyan, 2005. "Subgame Consistent Solutions of a Cooperative Stochastic Differential Game with Nontransferable Payoffs," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 701-724, March.
    2. Leon A Petrosyan & Nikolay A Zenkevich, 2016. "Game Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9824, December.
    3. D. W. K. Yeung & L. A. Petrosyan, 2004. "Subgame Consistent Cooperative Solutions in Stochastic Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 651-666, March.
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    Citations

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    Cited by:

    1. David W. K. Yeung & Leon A. Petrosyan, 2016. "A Cooperative Dynamic Environmental Game of Subgame Consistent Clean Technology Development," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-23, June.
    2. D. W. K. Yeung & L. A. Petrosyan, 2011. "Subgame Consistent Cooperative Solution of Dynamic Games with Random Horizon," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 78-97, July.
    3. David Yeung, 2014. "Dynamically consistent collaborative environmental management with production technique choices," Annals of Operations Research, Springer, vol. 220(1), pages 181-204, September.
    4. 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.
    5. David Yeung & Ovanes Petrosian, 2017. "Infinite Horizon Dynamic Games: A New Approach via Information Updating," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-23, December.
    6. Leon A. Petrosyan & David W.K. Yeung, 2020. "Cooperative Dynamic Games with Durable Controls: Theory and Application," Dynamic Games and Applications, Springer, vol. 10(4), pages 872-896, December.
    7. David W. K. Yeung & Leon A. Petrosyan, 2019. "Cooperative Dynamic Games with Control Lags," Dynamic Games and Applications, Springer, vol. 9(2), pages 550-567, June.

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