IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v318y2022i2d10.1007_s10479-020-03916-x.html
   My bibliography  Save this article

Stackelberg-Nash equilibrium and quasi harmonic games

Author

Listed:
  • Lina Mallozzi

    (University of Naples Federico II)

  • Armando Sacco

    (University of Naples “Parthenope”)

Abstract

Security solutions for two stage games, where the second stage consists of a strategic form noncooperative game, are not reachable in many problems. The aim of this paper is to investigate such solutions. Mixed extension for the second stage game is considered and existence results for approximate mixed security solutions, together with the convergences of values, are given and illustrated by significative examples. The results apply to the class of quasi harmonic games.

Suggested Citation

  • Lina Mallozzi & Armando Sacco, 2022. "Stackelberg-Nash equilibrium and quasi harmonic games," Annals of Operations Research, Springer, vol. 318(2), pages 1029-1041, November.
    • Handle: RePEc:spr:annopr:v:318:y:2022:i:2:d:10.1007_s10479-020-03916-x
    DOI: 10.1007/s10479-020-03916-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-020-03916-x
    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/s10479-020-03916-x?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. Hanif D. Sherali & Allen L. Soyster & Frederic H. Murphy, 1983. "Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations," Operations Research, INFORMS, vol. 31(2), pages 253-276, April.
    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. Lina Mallozzi & Jacqueline Morgan, 2006. "On approximate mixed Nash equilibria and average marginal functions for two-stage three-players games," Springer Optimization and Its Applications, in: Stephan Dempe & Vyacheslav Kalashnikov (ed.), Optimization with Multivalued Mappings, pages 97-107, Springer.
    4. Ozan Candogan & Ishai Menache & Asuman Ozdaglar & Pablo A. Parrilo, 2011. "Flows and Decompositions of Games: Harmonic and Potential Games," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 474-503, August.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. Juan S. Borrero & Oleg A. Prokopyev & Denis Sauré, 2019. "Sequential Interdiction with Incomplete Information and Learning," Operations Research, INFORMS, vol. 67(1), pages 72-89, January.
    4. Lina Mallozzi & Panos M. Pardalos, 2022. "Entropic Regularization in Hierarchical Games," SN Operations Research Forum, Springer, vol. 3(1), pages 1-14, March.
    5. Onur Tavaslıoğlu & Oleg A. Prokopyev & Andrew J. Schaefer, 2019. "Solving Stochastic and Bilevel Mixed-Integer Programs via a Generalized Value Function," Operations Research, INFORMS, vol. 67(6), pages 1659-1677, November.
    6. Lv, Chengwei & Xu, Jiuping & Xie, Heping & Zeng, Ziqiang & Wu, Yimin, 2016. "Equilibrium strategy based coal blending method for combined carbon and PM10 emissions reductions," Applied Energy, Elsevier, vol. 183(C), pages 1035-1052.
    7. 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.
    8. 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).
    9. 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).
    10. Hafezalkotob, Ashkan, 2017. "Competition of domestic manufacturer and foreign supplier under sustainable development objectives of government," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 294-308.
    11. 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.
    12. 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.
    13. 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".
    14. 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.
    15. 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.
    16. Lei Fang & Hecheng Li, 2013. "Lower bound of cost efficiency measure in DEA with incomplete price information," Journal of Productivity Analysis, Springer, vol. 40(2), pages 219-226, October.
    17. Vivek Laha & Harsh Narayan Singh, 2023. "On quasidifferentiable mathematical programs with equilibrium constraints," Computational Management Science, Springer, vol. 20(1), pages 1-20, December.
    18. Andreas Ehrenmann & Karsten Neuhoff, 2009. "A Comparison of Electricity Market Designs in Networks," Operations Research, INFORMS, vol. 57(2), pages 274-286, April.
    19. Nair, Rahul & Miller-Hooks, Elise, 2014. "Equilibrium network design of shared-vehicle systems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 47-61.
    20. Mahdi Zarghami & Nasim Safari & Ferenc Szidarovszky & Shafiqul Islam, 2015. "Nonlinear Interval Parameter Programming Combined with Cooperative Games: a Tool for Addressing Uncertainty in Water Allocation Using Water Diplomacy Framework," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(12), pages 4285-4303, September.

    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:318:y:2022:i:2:d:10.1007_s10479-020-03916-x. 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.