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Stackelberg Solutions of Feedback Type for Differential Games with Random Initial Data

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  • Alberto Bressan
  • Deling Wei

Abstract

The paper is concerned with Stackelberg solutions for a differential game with deterministic dynamics but random initial data, where the leading player can adopt a strategy in feedback form: u 1 =u 1 (t,x). The first main result provides the existence of a Stackelberg equilibrium solution, assuming that the family of feedback controls u 1 (t,⋅) available to the leading player are constrained to a finite dimensional space. A second theorem provides necessary conditions for the optimality of a feedback strategy. Finally, in the case where the feedback u 1 is allowed to be an arbitrary function, an example illustrates a wide class of systems where the minimal cost for the leading player corresponds to an impulsive dynamics. In this case, a Stackelberg equilibrium solution does not exist, but a minimizing sequence of strategies can be described. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Alberto Bressan & Deling Wei, 2013. "Stackelberg Solutions of Feedback Type for Differential Games with Random Initial Data," Dynamic Games and Applications, Springer, vol. 3(3), pages 341-358, September.
    • Handle: RePEc:spr:dyngam:v:3:y:2013:i:3:p:341-358
    DOI: 10.1007/s13235-012-0063-6
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    References listed on IDEAS

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    1. P. Cardaliaguet & M. Quincampoix, 2008. "Deterministic Differential Games Under Probability Knowledge Of Initial Condition," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 1-16.
    2. Alberto Bressan & Wen Shen, 2004. "Semi-cooperative strategies for differential games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 561-593, August.
    3. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
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    Cited by:

    1. Richárd Kicsiny, 2017. "Solution for a class of closed-loop leader-follower games with convexity conditions on the payoffs," Annals of Operations Research, Springer, vol. 253(1), pages 405-429, June.
    2. Alberto Bressan & Yilun Jiang, 2020. "Self-consistent Feedback Stackelberg Equilibria for Infinite Horizon Stochastic Games," Dynamic Games and Applications, Springer, vol. 10(2), pages 328-360, June.

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