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Subgame Consistent Cooperative Solution of Dynamic Games with Random Horizon

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)

Abstract

In cooperative dynamic games, a stringent condition—that of subgame consistency—is required for a dynamically stable cooperative solution. In particular, under a subgame-consistent cooperative solution an extension of the solution policy to a subgame starting at a later time with a state brought about by prior optimal behavior will remain optimal. This paper extends subgame-consistent solutions to dynamic (discrete-time) cooperative games with random horizon. In the analysis, new forms of the Bellman equation and the Isaacs–Bellman equation in discrete-time are derived. Subgame-consistent cooperative solutions are obtained for this class of 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 dynamic games with random horizon are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:1:d:10.1007_s10957-011-9824-4
    DOI: 10.1007/s10957-011-9824-4
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    References listed on IDEAS

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    1. J. B. Krawczyk & M. Tidball, 2006. "A Discrete-Time Dynamic Game of Seasonal Water Allocation," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 411-429, February.
    2. Nie, Pu-yan & Chen, Li-hua & Fukushima, Masao, 2006. "Dynamic programming approach to discrete time dynamic feedback Stackelberg games with independent and dependent followers," European Journal of Operational Research, Elsevier, vol. 169(1), pages 310-328, February.
    3. D. W. K. Yeung, 2007. "Dynamically Consistent Cooperative Solution in a Differential Game of Transboundary Industrial Pollution," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 143-160, July.
    4. Basar, Tamer & Ho, Yu-Chi, 1974. "Informational properties of the Nash solutions of two stochastic nonzero-sum games," Journal of Economic Theory, Elsevier, vol. 7(4), pages 370-387, April.
    5. Engelbert J. Dockner & Kazuo Nishimura, 1999. "Transboundary Pollution in a Dynamic Game Model," The Japanese Economic Review, Japanese Economic Association, vol. 50(4), pages 443-456, December.
    6. Rubio, Santiago J. & Ulph, Alistair, 2007. "An infinite-horizon model of dynamic membership of international environmental agreements," Journal of Environmental Economics and Management, Elsevier, vol. 54(3), pages 296-310, November.
    7. 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.
    8. Prajit Dutta & Roy Radner, 2006. "Population growth and technological change in a global warming model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 251-270, October.
    9. Ehtamo, Harri & Hamalainen, Raimo P., 1993. "A cooperative incentive equilibrium for a resource management problem," Journal of Economic Dynamics and Control, Elsevier, vol. 17(4), pages 659-678, July.
    10. 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.
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    Cited by:

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    2. Ovanes Petrosian & Lihong Shi & Yin Li & Hongwei Gao, 2019. "Moving Information Horizon Approach for Dynamic Game Models," Mathematics, MDPI, vol. 7(12), pages 1-31, December.
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    4. Elena M. Parilina & Georges Zaccour, 2017. "Node-Consistent Shapley Value for Games Played over Event Trees with Random Terminal Time," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 236-254, October.
    5. 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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