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Stackelberg Solutions of Differential Games in the Class of Nonanticipative Strategies

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  • Yurii Averboukh
  • Artem Baklanov

Abstract

The reverse Stackelberg solution of a two-person nonzero-sum differential game is considered. We assume that the leader plays in the class of nonanticipative strategies. The main result is the description of the Stackelberg solutions via an auxiliary zero-sum differential game. The case when the leader’s strategies depend on the actual control of the follower is compared with the case when the leader uses nonanticipative strategies. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Yurii Averboukh & Artem Baklanov, 2014. "Stackelberg Solutions of Differential Games in the Class of Nonanticipative Strategies," Dynamic Games and Applications, Springer, vol. 4(1), pages 1-9, March.
    • Handle: RePEc:spr:dyngam:v:4:y:2014:i:1:p:1-9
    DOI: 10.1007/s13235-013-0077-8
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    References listed on IDEAS

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    1. G. J. Olsder, 2009. "Phenomena in Inverse Stackelberg Games, Part 2: Dynamic Problems," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 601-618, December.
    2. Piernicola Bettiol & Pierre Cardaliaguet & Marc Quincampoix, 2006. "Zero-sum state constrained differential games: existence of value for Bolza problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(4), pages 495-527, November.
    3. G. J. Olsder, 2009. "Phenomena in Inverse Stackelberg Games, Part 1: Static Problems," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 589-600, December.
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    Cited by:

    1. Fuxiao Lu & Guowei Liu & Jianxiong Zhang & Wansheng Tang, 2016. "Benefits of partial myopia in a durable product supply chain considering pricing and advertising," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(10), pages 1309-1324, October.
    2. Yurii Averboukh, 2018. "Inverse Stackelberg Solutions for Games with Many Followers," Mathematics, MDPI, vol. 6(9), pages 1-9, August.
    3. 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.

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