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Multilevel Reverse Stackelberg Differential Games: Existence and Solution Approach for Affine Strategies

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Abstract

This article considers multilevel sequential differential games over fixed time interval. In this continuous time game structure, the leader controls the outcome by announcing a reverse Stackelberg strategy as a mapping from the decision spaces of the followers to his/her decision space. The leader constructs such a strategy based on the control of the followers, which can be determined up to the current time only, also called causal strategy. Existence of affine reverse Stackelberg strategy for multilevel differential games is proved, and a method to obtain such set of strategies is also presented. The structure of this game can be adopted to many application areas, in particular in decentralized continuous decision making situations such as marketing system, taxation and budget allocation. As compared to the existing literature, the result applies to more general game settings and hierarchical levels of decisions.

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Acknowledgements

The authors would like to thank the anonymous referees and the area editors whose comments and suggestions improved this final version of our paper.

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Authors and Affiliations

  1. Department of Mathematics, Bahir Dar University, P.O.Box 79, Bahir Dar, Ethiopia

    Seyfe Belete Worku & Birilew Belayneh Tsegaw

  2. Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, P/Bag 16, Palapye, Botswana

    Semu Mitiku Kassa

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  1. Seyfe Belete Worku
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  2. Birilew Belayneh Tsegaw
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Correspondence to Semu Mitiku Kassa.

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Communicated by Bruce A. Conway.

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Worku, S.B., Tsegaw, B.B. & Kassa, S.M. Multilevel Reverse Stackelberg Differential Games: Existence and Solution Approach for Affine Strategies. J Optim Theory Appl 196, 617–640 (2023). https://doi.org/10.1007/s10957-022-02149-1

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