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Existence and computations of best affine strategies for multilevel reverse Stackelberg games

Author

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  • Seyfe Belete Worku

    (Bahir Dar University)

  • Birilew Belayneh Tsegaw

    (Bahir Dar University)

  • Semu Mitiku Kassa

    (Botswana International University of Science and Technology)

Abstract

The multilevel reverse Stackelberg game is considered. In this game, the leader controls the outcome by announcing a strategy as a function of decision variables of the followers to his/her own decision space. Corresponding to the leader’s strategy, the player in the next level presents his/her strategy as a function of decision variables of the remaining players. This procedure is repeated until it is the turn of the bottom level player in the hierarchy, who reacts by determining his/her optimal decision variables. The structure of this game can be adopted in decentralized multilevel decision making like resource allocation, energy market pricing, problems with hierarchical controls. In this paper conditions for existence and construction of affine leader reverse Stackelberg strategies are developed for such problems. As an extension to the existing literature, we considered nonconvex sublevel sets of objective functions of followers. Moreover, a method to construct multiple reverse Stackelberg strategies for the leader is also presented.

Suggested Citation

  • Seyfe Belete Worku & Birilew Belayneh Tsegaw & Semu Mitiku Kassa, 2023. "Existence and computations of best affine strategies for multilevel reverse Stackelberg games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 339-366, June.
    • Handle: RePEc:spr:mathme:v:97:y:2023:i:3:d:10.1007_s00186-023-00820-5
    DOI: 10.1007/s00186-023-00820-5
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    References listed on IDEAS

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    1. Noortje Groot & Bart Schutter & Hans Hellendoorn, 2016. "Optimal Affine Leader Functions in Reverse Stackelberg Games," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 348-374, January.
    2. 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.
    3. Abay Molla Kassa & Semu Mitiku Kassa, 2017. "Deterministic solution approach for some classes of nonlinear multilevel programs with multiple followers," Journal of Global Optimization, Springer, vol. 68(4), pages 729-747, August.
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