IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v168y2016i1d10.1007_s10957-014-0694-4.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-014-0694-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-014-0694-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Engwerda, J.C., 2012. "Prospects of Tools from Differential Games in the Study Of Macroeconomics of Climate Change," Other publications TiSEM cac36d07-227b-4cf2-83cb-7, Tilburg University, School of Economics and Management.
    2. Yurii Averboukh, 2018. "Inverse Stackelberg Solutions for Games with Many Followers," Mathematics, MDPI, vol. 6(9), pages 1-9, August.
    3. Yifen Mu, 2014. "Inverse Stackelberg Public Goods Game with Multiple Hierarchies Under Global and Local Information Structures," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 332-350, October.
    4. Grigory Belyavsky & Natalya Danilova & Guennady Ougolnitsky, 2018. "A Markovian Mechanism of Proportional Resource Allocation in the Incentive Model as a Dynamic Stochastic Inverse Stackelberg Game," Mathematics, MDPI, vol. 6(8), pages 1-10, July.
    5. Olga Gorbaneva & Guennady Ougolnitsky, 2022. "Sustainability of Intertwined Supply Networks: A Game-Theoretic Approach," Games, MDPI, vol. 13(3), pages 1-21, April.
    6. Babajanyan, S.G. & Melkikh, A.V. & Allahverdyan, A.E., 2020. "Leadership scenarios in prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    7. 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.
    8. Guennady Ougolnitsky & Anatoly Usov, 2023. "Differential Game-Theoretic Models of Cournot Oligopoly with Consideration of the Green Effect," Games, MDPI, vol. 14(1), pages 1-18, January.
    9. Carvalho, Margarida & Lodi, Andrea, 2023. "A theoretical and computational equilibria analysis of a multi-player kidney exchange program," European Journal of Operational Research, Elsevier, vol. 305(1), pages 373-385.
    10. Andreas Lanz & Gregor Reich & Ole Wilms, 2022. "Adaptive grids for the estimation of dynamic models," Quantitative Marketing and Economics (QME), Springer, vol. 20(2), pages 179-238, June.
    11. Shi, Yi & Deng, Yawen & Wang, Guoan & Xu, Jiuping, 2020. "Stackelberg equilibrium-based eco-economic approach for sustainable development of kitchen waste disposal with subsidy policy: A case study from China," Energy, Elsevier, vol. 196(C).
    12. Lucio Bianco & Massimiliano Caramia & Stefano Giordani & Veronica Piccialli, 2016. "A Game-Theoretic Approach for Regulating Hazmat Transportation," Transportation Science, INFORMS, vol. 50(2), pages 424-438, May.
    13. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    14. Xu, Jiuping & Shu, Kejing & Wang, Fengjuan & Yang, Guocan, 2024. "Bi-level multi-objective distribution strategy integrating the permit trading scheme towards coal production capacity layout optimization: Case study from China," Resources Policy, Elsevier, vol. 91(C).
    15. Cerulli, Martina & Serra, Domenico & Sorgente, Carmine & Archetti, Claudia & Ljubić, Ivana, 2023. "Mathematical programming formulations for the Collapsed k-Core Problem," European Journal of Operational Research, Elsevier, vol. 311(1), pages 56-72.
    16. Chan Y. Han & Brian J. Lunday & Matthew J. Robbins, 2016. "A Game Theoretic Model for the Optimal Location of Integrated Air Defense System Missile Batteries," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 405-416, August.
    17. Lorenzo Lampariello & Simone Sagratella, 2015. "It is a matter of hierarchy: a Nash equilibrium problem perspective on bilevel programming," DIAG Technical Reports 2015-07, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    18. R. Paulavičius & C. S. Adjiman, 2020. "New bounding schemes and algorithmic options for the Branch-and-Sandwich algorithm," Journal of Global Optimization, Springer, vol. 77(2), pages 197-225, June.
    19. Grimm, Veronika & Schewe, Lars & Schmidt, Martin & Zöttl, Gregor, 2017. "Uniqueness of market equilibrium on a network: A peak-load pricing approach," European Journal of Operational Research, Elsevier, vol. 261(3), pages 971-983.
    20. Wei Jiang & Huiqiang Wang & Bingyang Li & Haibin Lv & Qingchuan Meng, 2020. "A multi-user multi-operator computing pricing method for Internet of things based on bi-level optimization," International Journal of Distributed Sensor Networks, , vol. 16(1), pages 15501477199, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:168:y:2016:i:1:d:10.1007_s10957-014-0694-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.