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Cooperative Dynamic Games with Control Lags

Author

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  • David W. K. Yeung

    (St Petersburg State University
    Hong Kong Shue Yan University)

  • Leon A. Petrosyan

    (St Petersburg State University)

Abstract

Controls with lags are control strategies with prolonged effects lasting for more than one stage of the game after the controls had been executed. Lags in controls yielding adverse effects often make the negative impacts more significant. Cooperation provides an effective means to alleviate the problem and obtains an optimal solution. This paper extends the existing paradigm in cooperative dynamic games by allowing the existence of controls with lag effects on the players’ payoffs in subsequent stages. A novel dynamic optimization theorem with control lags is developed to derive the Pareto optimal cooperative controls. Subgame consistent solutions are derived to ensure sustainable cooperation. In particular, subgame consistency guarantees that the optimality principle agreed upon at the outset will remain effective throughout the game and, hence, there is no incentive for any player to deviate from cooperation scheme. A procedure for imputation distribution is provided to formulate a dynamically stable cooperative scheme under control lags. An application in cooperative environmental management is presented. This is the first time that cooperative dynamic games with control lags are studied.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:2:d:10.1007_s13235-018-0266-6
    DOI: 10.1007/s13235-018-0266-6
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    References listed on IDEAS

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    1. Ulrich Brandt-Pollmann & Ralph Winkler & Sebastian Sager & Ulf Moslener & Johannes Schlöder, 2008. "Numerical Solution of Optimal Control Problems with Constant Control Delays," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 181-206, March.
    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. David W.K. Yeung & Leon A. Petrosyan, 2016. "Subgame Consistent Cooperation," Theory and Decision Library C, Springer, number 978-981-10-1545-8, March.
    5. 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:

    1. 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.

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