IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v253y2017i1d10.1007_s10479-016-2327-9.html
   My bibliography  Save this article

Solution for a class of closed-loop leader-follower games with convexity conditions on the payoffs

Author

Listed:
  • Richárd Kicsiny

    (Szent István University)

Abstract

In the present paper, a recent deterministic continuum-strategy two-player discrete-time dynamic leader-follower game with fixed finite time duration and closed-loop information structure is studied. The types of the considered payoff functions can be widely used in different applications (mainly in conflicts of consuming a limited resource, where one player, called the leader, is a superior authority choosing a strategy choice first, and another player, called the follower, chooses after). In case of certain payoff convexity, explicit conditions are given, when it can be known in advance that an equilibrium exists and consists of only two possible choices of both players at each step. The sub-game equilibrium from a given step may depend on the former selections of the players. Thus the continuum-strategy problem has been reduced to a general finite game of two possible choices corresponding to both players. Such type of games could be solved in a standard way with dynamic programming using a computer. Nevertheless, the game can be further simplified, and then an equilibrium can be directly determined, such decreasing the computational demand to a great extent. A solution algorithm and practical examples are also given to support the real-life application of the results.

Suggested Citation

  • Richárd Kicsiny, 2017. "Solution for a class of closed-loop leader-follower games with convexity conditions on the payoffs," Annals of Operations Research, Springer, vol. 253(1), pages 405-429, June.
    • Handle: RePEc:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2327-9
    DOI: 10.1007/s10479-016-2327-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-016-2327-9
    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/s10479-016-2327-9?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. Kicsiny, R. & Varga, Z. & Scarelli, A., 2014. "Backward induction algorithm for a class of closed-loop Stackelberg games," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1021-1036.
    2. Romano, Richard & Yildirim, Huseyin, 2005. "On the endogeneity of Cournot-Nash and Stackelberg equilibria: games of accumulation," Journal of Economic Theory, Elsevier, vol. 120(1), pages 73-107, January.
    3. Rabah Amir & Giuseppe Feo, 2014. "Endogenous timing in a mixed duopoly," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 629-658, August.
    4. Sharma, Yogeshwer & Williamson, David P., 2009. "Stackelberg thresholds in network routing games or the value of altruism," Games and Economic Behavior, Elsevier, vol. 67(1), pages 174-190, September.
    5. Heinrich von Stackelberg, 2011. "Market Structure and Equilibrium," Springer Books, Springer, number 978-3-642-12586-7, December.
    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. Jerome Adda & Russell W. Cooper, 2003. "Dynamic Economics: Quantitative Methods and Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012014, December.
    8. Parimal Bag & Santanu Roy, 2011. "On sequential and simultaneous contributions under incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 119-145, February.
    9. Moshe Bar Niv & Israel Zang, 1999. ""Costless" regulation of monopolies with large entry cost: A game theoretic approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 35-52.
    10. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    11. Du, Gang & Jiao, Roger J. & Chen, Mo, 2014. "Joint optimization of product family configuration and scaling design by Stackelberg game," European Journal of Operational Research, Elsevier, vol. 232(2), pages 330-341.
    12. Alemdar, Nedim M. & Sirakaya, Sibel, 2003. "On-line computation of Stackelberg equilibria with synchronous parallel genetic algorithms," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1503-1515, June.
    13. Nie, Pu-yan & Chen, Li-hua & Fukushima, Masao, 2006. "Dynamic programming approach to discrete time dynamic feedback Stackelberg games with independent and dependent followers," European Journal of Operational Research, Elsevier, vol. 169(1), pages 310-328, February.
    14. Alberto Bressan & Deling Wei, 2013. "Stackelberg Solutions of Feedback Type for Differential Games with Random Initial Data," Dynamic Games and Applications, Springer, vol. 3(3), pages 341-358, September.
    15. Damien J. A. Bazin, 2011. "Marketstructure and equilibrium," Post-Print halshs-00727586, HAL.
    16. Dastidar, Krishnendu Ghosh, 2004. "On Stackelberg games in a homogeneous product market," European Economic Review, Elsevier, vol. 48(3), pages 549-562, June.
    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. Kicsiny, R., 2019. "Differential game model with discretized solution for distributing heat produced by solar heating systems," Renewable Energy, Elsevier, vol. 140(C), pages 330-340.
    2. Richárd Kicsiny & Levente Hufnagel & Zoltán Varga, 2023. "Allocation of limited resources under quadratic constraints," Annals of Operations Research, Springer, vol. 322(2), pages 793-817, March.
    3. de Frutos Cachorro, Julia & Martín-Herrán, Guiomar & Tidball, Mabel, 2024. "Commitment vs. noncommitment behaviors in natural resource conflicts: A case study of groundwater resources," Economic Modelling, Elsevier, vol. 132(C).
    4. Julia de Frutos Cachorro & Guiomar Martín-Herrán & Mabel Tidball, 2022. "Stackelberg competition in groundwater resources with multiple uses," UB School of Economics Working Papers 2022/431, University of Barcelona School of Economics.
    5. Richárd Kicsiny & Zoltán Varga, 2023. "New algorithm for checking Pareto optimality in bimatrix games," Annals of Operations Research, Springer, vol. 320(1), pages 235-259, January.

    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. Kicsiny, R. & Varga, Z. & Scarelli, A., 2014. "Backward induction algorithm for a class of closed-loop Stackelberg games," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1021-1036.
    2. 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.
    3. Julien, Ludovic A., 2017. "On noncooperative oligopoly equilibrium in the multiple leader–follower game," European Journal of Operational Research, Elsevier, vol. 256(2), pages 650-662.
    4. Gang Du & Yi Xia & Roger J. Jiao & Xiaojie Liu, 2019. "Leader-follower joint optimization problems in product family design," Journal of Intelligent Manufacturing, Springer, vol. 30(3), pages 1387-1405, March.
    5. Magnus Hoffmann & Grégoire Rota‐Graziosi, 2020. "Endogenous timing in the presence of non‐monotonicities," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(1), pages 359-402, February.
    6. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2021. "A Local Variation Method for Bilevel Nash Equilibrium Problems," CSEF Working Papers 620, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    7. Francesco Caruso & M. Beatrice Lignola & Jacqueline Morgan, 2020. "Regularization and Approximation Methods in Stackelberg Games and Bilevel Optimization," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 77-138, Springer.
    8. Zhu, Lijing & Zhang, Qi & Lu, Huihui & Li, Hailong & Li, Yan & McLellan, Benjamin & Pan, Xunzhang, 2017. "Study on crowdfunding’s promoting effect on the expansion of electric vehicle charging piles based on game theory analysis," Applied Energy, Elsevier, vol. 196(C), pages 238-248.
    9. Robert P. Gilles & Lina Mallozzi & Roberta Messalli, 2021. "Emergent Collaboration in Social Purpose Games," Papers 2109.08471, arXiv.org.
    10. Casorrán, Carlos & Fortz, Bernard & Labbé, Martine & Ordóñez, Fernando, 2019. "A study of general and security Stackelberg game formulations," European Journal of Operational Research, Elsevier, vol. 278(3), pages 855-868.
    11. Yuji Aruka, 2018. "Interpreting the iterated dilemma games using the presentation like “cellular automatons”," Evolutionary and Institutional Economics Review, Springer, vol. 15(2), pages 351-365, December.
    12. Zhisong Chen & Keith C. K. Cheung & Xiangtong Qi, 2021. "Subsidy policies and operational strategies for multiple competing photovoltaic supply chains," Flexible Services and Manufacturing Journal, Springer, vol. 33(4), pages 914-955, December.
    13. Ashantha Ranasinghe & Xuejuan Su, 2023. "When social assistance meets market power: A mixed duopoly view of health insurance in the United States," Economic Inquiry, Western Economic Association International, vol. 61(4), pages 851-869, October.
    14. 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.
    15. 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.
    16. 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).
    17. Oleksandr Shcherbakov, 2022. "Firm‐level investment under imperfect capital markets in Ukraine," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 31(1), pages 227-255, February.
    18. 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.
    19. 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.
    20. Fell, Harrison, 2016. "Comparing policies to confront permit over-allocation," Journal of Environmental Economics and Management, Elsevier, vol. 80(C), pages 53-68.

    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:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2327-9. 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.