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Subgame Consistent Solutions of a Cooperative Stochastic Differential Game with Nontransferable Payoffs

Author

Listed:
  • D.W.K. Yeung

    (Decision Sciences,Center for Game Theory)

  • L.A. Petrosyan

    (Applied Mathematics and Control Processes, Center for Game Theory)

Abstract

Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that the extension of the solution policy to a later starting time and any possible state brought about by the prior optimal behavior of the players would remain optimal. Recently, mechanisms for the derivation of subgame consistent solutions in stochastic cooperative differential games with transferable payoffs have been found. In this paper, subgame consistent solutions are derived for a class of cooperative stochastic differential games with nontransferable payoffs. The previously intractable subgame consistent solution for games with nontransferable payoffs is rendered tractable.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:3:d:10.1007_s10957-004-1181-0
    DOI: 10.1007/s10957-004-1181-0
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    References listed on IDEAS

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    1. Alain Haurie & Jacek B Krawczyk & Georges Zaccour, 2012. "Differential Games," World Scientific Book Chapters, in: Games and Dynamic Games, chapter 7, pages 243-302, World Scientific Publishing Co. Pte. Ltd..
    2. D. W. K. Yeung, 2001. "Infinite-Horizon Stochastic Differential Games with Branching Payoffs," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 445-460, November.
    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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    Cited by:

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    2. Engwerda, J.C., 2007. "A Note on Cooperative Linear Quadratic Control," Other publications TiSEM 7b5b1ece-b947-4ad0-9489-1, Tilburg University, School of Economics and Management.
    3. Engwerda, J.C., 2007. "Necessary and Sufficient Conditions for Solving Cooperative Differential Games," Other publications TiSEM 048f8662-e7ce-48af-9e5a-8, Tilburg University, School of Economics and Management.
    4. David Yeung, 2014. "Dynamically consistent collaborative environmental management with production technique choices," Annals of Operations Research, Springer, vol. 220(1), pages 181-204, September.
    5. Engwerda, J.C., 2007. "Multicriteria Dynamic Optimization Problems and Cooperative Dynamic Games," Discussion Paper 2007-41, Tilburg University, Center for Economic Research.
    6. 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.
    7. Elena M. Parilina & Puduru Viswanadha Reddy & Georges Zaccour, 2022. "Endogenous Duration of Long-term Agreements in Cooperative Dynamic Games with Nontransferable Utility," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 808-836, December.

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