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Phenomena in Inverse Stackelberg Games, Part 1: Static Problems

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  • G. J. Olsder

    (Delft University of Technology)

Abstract

Games are considered in which the role of the players is a hierarchical one. Some players behave as leaders, others as followers. Such games are named after Stackelberg. In the current paper, a special type of these games is considered, known in the literature as inverse Stackelberg games. In such games, the leader (or: leaders) announces his strategy as a mapping from the follower (or: followers) decision space into his own decision space. Arguments for studying such problems are given. The routine way of analysis, leading to a study of composed functions, is not very fruitful. Other approaches are given, mainly by studying specific examples. Phenomena in problems with more than one leader and/or follower are studied within the context of the inverse Stackelberg concept. As a side issue, expressions like “two captains on a ship” and “divide and conquer” are given a mathematical foundation.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:3:d:10.1007_s10957-009-9573-9
    DOI: 10.1007/s10957-009-9573-9
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    References listed on IDEAS

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    1. Epstein, Gil S & Hefeker, Carsten, 2001. "Lobbying and Concessions: Comparing Nash to Stackelberg Games," Public Choice, Springer, vol. 109(1-2), pages 175-181, October.
    2. 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.
    3. Geert Jan Olsder, 2000. "Differential Game-Theoretic Thoughts On Option Pricing And Transaction Costs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(02n03), pages 209-228.
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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.
    2. 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).
    3. Olga Gorbaneva & Guennady Ougolnitsky, 2022. "Sustainability of Intertwined Supply Networks: A Game-Theoretic Approach," Games, MDPI, vol. 13(3), pages 1-21, April.
    4. Yurii Averboukh, 2018. "Inverse Stackelberg Solutions for Games with Many Followers," Mathematics, MDPI, vol. 6(9), pages 1-9, August.
    5. 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.
    6. 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.
    7. 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.
    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. Engwerda, J.C., 2012. "Prospects of Tools from Differential Games in the Study Of Macroeconomics of Climate Change," Discussion Paper 2012-045, Tilburg University, Center for Economic Research.
    10. Seyfe Belete Worku & Birilew Belayneh Tsegaw & Semu Mitiku Kassa, 2023. "Multilevel Reverse Stackelberg Differential Games: Existence and Solution Approach for Affine Strategies," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 617-640, February.
    11. 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.
    12. 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.
    13. Liu, Yuan & He, Li & Shen, Jing, 2017. "Optimization-based provincial hybrid renewable and non-renewable energy planning – A case study of Shanxi, China," Energy, Elsevier, vol. 128(C), pages 839-856.

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