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Phenomena in Inverse Stackelberg Games, Part 2: Dynamic Problems

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  • G. J. Olsder

    (Delft University of Technology)

Abstract

Dynamic two-person games are considered, in which the roles of the players are hierarchical. One player behaves as a leader, the other one as a follower. Such games are named after Stackelberg. In the current paper, a special type of such games is considered, known in the literature as inverse Stackelberg games. In such games, the leader announces his strategy as a mapping from the follower’s decision space into his own decision space. Arguments for studying such problems are given. This paper specifically studies dynamic games, i.e. the underlying model is described by an ordinary differential equation. The decisions of both players have a time component. As in the static case, 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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:3:d:10.1007_s10957-009-9572-x
    DOI: 10.1007/s10957-009-9572-x
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    References listed on IDEAS

    as
    1. 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.
    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.
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    Cited by:

    1. 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).
    2. Olga Gorbaneva & Guennady Ougolnitsky, 2022. "Sustainability of Intertwined Supply Networks: A Game-Theoretic Approach," Games, MDPI, vol. 13(3), pages 1-21, April.
    3. Yurii Averboukh, 2018. "Inverse Stackelberg Solutions for Games with Many Followers," Mathematics, MDPI, vol. 6(9), pages 1-9, August.
    4. 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.
    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. 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.
    8. 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.
    9. Guennady Ougolnitsky & Anatoly Usov, 2019. "Spatially Distributed Differential Game Theoretic Model of Fisheries," Mathematics, MDPI, vol. 7(8), pages 1-13, August.
    10. 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.
    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. Elena Goncharova & Maxim Staritsyn, 2015. "Invariant Solutions of Differential Games with Measures: A Discontinuous Time Reparameterization Approach," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 382-400, October.

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