IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v237y2014i3p1021-1036.html

Backward induction algorithm for a class of closed-loop Stackelberg games

Author

Listed:
  • Kicsiny, R.
  • Varga, Z.
  • Scarelli, A.

Abstract

In the paper a new deterministic continuum-strategy two-player discrete-time dynamic Stackelberg game is proposed with fixed finite time duration and closed-loop information structure. The considered payoff functions can be widely used in different applications (mainly in conflicts of consuming a limited resource, where one player, called leader, is a superior authority choosing strategy first, and another player, called follower, chooses after).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:237:y:2014:i:3:p:1021-1036
    DOI: 10.1016/j.ejor.2014.02.057
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221714001921
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.02.057?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Benchekroun, Hassan & Withagen, Cees, 2012. "On price taking behavior in a nonrenewable resource cartel–fringe game," Games and Economic Behavior, Elsevier, vol. 76(2), pages 355-374.
    2. 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.
    3. Huck, Steffen & Muller, Wieland & Normann, Hans-Theo, 2001. "Stackelberg Beats Cournot: On Collusion and Efficiency in Experimental Markets," Economic Journal, Royal Economic Society, vol. 111(474), pages 749-765, October.
    4. 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.
    5. 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.
    6. 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.
    7. Colman, Andrew M. & Stirk, Jonathan A., 1998. "Stackelberg reasoning in mixed-motive games: An experimental investigation," Journal of Economic Psychology, Elsevier, vol. 19(2), pages 279-293, April.
    8. 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.
    9. Heinrich von Stackelberg, 2011. "Market Structure and Equilibrium," Springer Books, Springer, number 978-3-642-12586-7, October.
    10. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
    11. G. Freiling & G. Jank & S. R. Lee, 2001. "Existence and Uniqueness of Open-Loop Stackelberg Equilibria in Linear-Quadratic Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 515-544, September.
    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. Hoffmann, Magnus & Rota-Graziosi, Grégoire, 2012. "Endogenous timing in general rent-seeking and conflict models," Games and Economic Behavior, Elsevier, vol. 75(1), pages 168-184.
    14. 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. 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.
    3. Nematollahi, Mohammadreza & Guitouni, Adel & Heydari, Jafar & Gerbrandt, Eric M., 2025. "win–win contract farming in dual-channel agribusiness supply chains under yield, quality, and price uncertainty," International Journal of Production Economics, Elsevier, vol. 286(C).
    4. 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.
    5. Liang Shen & Runjie Fan & Zhaoqing Yu & Yuyan Wang, 2021. "The Service Strategy and Influencing Factors of Online Recycling of Used Mobile Phones," Mathematics, MDPI, vol. 9(21), pages 1-24, October.
    6. 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.
    7. Chen, Yang & Park, Byungkwon & Kou, Xiao & Hu, Mengqi & Dong, Jin & Li, Fangxing & Amasyali, Kadir & Olama, Mohammed, 2020. "A comparison study on trading behavior and profit distribution in local energy transaction games," Applied Energy, Elsevier, vol. 280(C).
    8. Marian Leimbach & Anselm Schultes & Lavinia Baumstark & Anastasis Giannousakis & Gunnar Luderer, 2017. "Solution algorithms for regional interactions in large-scale integrated assessment models of climate change," Annals of Operations Research, Springer, vol. 255(1), pages 29-45, August.

    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. 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.
    2. 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.
    3. 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.
    4. Pau Balart & Sabine Flamand & Oliver Gürtler & Orestis Troumpounis, 2018. "Sequential choice of sharing rules in collective contests," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 20(5), pages 703-724, October.
    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. Colombo, Luca & Labrecciosa, Paola, 2019. "Stackelberg versus Cournot: A differential game approach," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 239-261.
    7. Hoffmann, Magnus & Rota-Graziosi, Grégoire, 2012. "Endogenous timing in general rent-seeking and conflict models," Games and Economic Behavior, Elsevier, vol. 75(1), pages 168-184.
    8. Cumbul, Eray, 2021. "Stackelberg versus Cournot oligopoly with private information," International Journal of Industrial Organization, Elsevier, vol. 74(C).
    9. Bade, Sophie & Haeringer, Guillaume & Renou, Ludovic, 2009. "Bilateral commitment," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1817-1831, July.
    10. Hörtnagl, Tanja & Kerschbamer, Rudolf & Stracke, Rudi, 2019. "Competing for market shares: Does the order of moves matter even when it shouldn’t?," Journal of Economic Behavior & Organization, Elsevier, vol. 166(C), pages 346-365.
    11. Makoto Yano & Takashi Komatsubara, 2018. "Price competition or price leadership," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(4), pages 1023-1057, December.
    12. Daniele Nosenzo & Martin Sefton, 2011. "Endogenous Move Structure and Voluntary Provision of Public Goods: Theory and Experiment," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 13(5), pages 721-754, October.
    13. Arozamena, Leandro & Weinschelbaum, Federico, 2009. "Simultaneous vs. sequential price competition with incomplete information," Economics Letters, Elsevier, vol. 104(1), pages 23-26, July.
    14. 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.
    15. Ciwei Dong & Liu Yang & Chi To Ng, 2020. "Quantity Leadership for a Dual-Channel Supply Chain with Retail Service," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(02), pages 1-32, March.
    16. 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.
    17. Gantner, Anita & Horn, Kristian & Kerschbamer, Rudolf, 2016. "Fair and efficient division through unanimity bargaining when claims are subjective," Journal of Economic Psychology, Elsevier, vol. 57(C), pages 56-73.
    18. Hoffmann, Magnus & Kolmar, Martin, 2017. "Distributional preferences in probabilistic and share contests," Journal of Economic Behavior & Organization, Elsevier, vol. 142(C), pages 120-139.
    19. Radzvilas, Mantas, 2016. "Hypothetical Bargaining and the Equilibrium Selection Problem in Non-Cooperative Games," MPRA Paper 70248, University Library of Munich, Germany.
    20. Guth, Werner & Ritzberger, Klaus & van Damme, Eric, 2004. "On the Nash bargaining solution with noise," European Economic Review, Elsevier, vol. 48(3), pages 697-713, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:ejores:v:237:y:2014:i:3:p:1021-1036. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.