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Optimal Affine Leader Functions in Reverse Stackelberg Games

Author

Listed:
  • Noortje Groot

    (Delft University of Technology)

  • Bart Schutter

    (Delft University of Technology)

  • Hans Hellendoorn

    (Delft University of Technology)

Abstract

A generalizing analysis is made in order to ease the solvability of the generally complex single-leader–single-follower reverse Stackelberg game. This game is of a hierarchical nature and can therefore be implemented as a structure for multi-level decision-making problems, like in road pricing. In particular, a leader function of the affine type is analyzed in order to procure a systematic approach to solving the game to optimality. To this end, necessary and sufficient existence conditions for this optimal affine leader function are developed. Compared to earlier results reported in the literature, differentiability of the follower objective functional is relaxed, and locally strict convexity of the sublevel set at the desired reverse Stackelberg equilibrium is replaced with the more general property of an exposed point. Moreover, a full characterization of the set of optimal affine leader functions that is derived, which use in the case of secondary optimization objectives as well as for a constrained decision space, is illustrated.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:1:d:10.1007_s10957-014-0694-4
    DOI: 10.1007/s10957-014-0694-4
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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. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    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. 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.

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