IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v479y2024ics0096300324003357.html
   My bibliography  Save this article

Matrix norm methods for zero-sum fuzzy matrix games with payoffs of triangular fuzzy numbers

Author

Listed:
  • İzgi, Burhaneddin
  • Kocken, Hale Gonce
  • Özkaya, Murat

Abstract

In this paper, we mainly consider the solution of two-person zero-sum fuzzy matrix games with payoffs of triangular fuzzy numbers. Contrary to the literature, we focus on developing the methods to solve the game directly based on only the norms of the payoff matrix holistically, without solving a linear programming problem or handling sub-games created by taking the components of fuzzy numbers separately. For this purpose, we first present fuzzy versions of 1-norm and ∞-norm with the help of a ranking function and develop the fuzzy matrix norm method to obtain an approximate solution of the zero-sum fuzzy matrix game. In addition to this approach, we provide the fuzzy extended matrix norm method as an enhanced version of the method, which involves the use of newly defined fuzzy matrix norms. Thus, we managed to avoid the complexity of the optimization process of the linear programming problem via the proposed matrix norm-based methods. Finally, we illustrate the implementation of the methods by considering several benchmark examples and a 3 × 3 fuzzy matrix game.

Suggested Citation

  • İzgi, Burhaneddin & Kocken, Hale Gonce & Özkaya, Murat, 2024. "Matrix norm methods for zero-sum fuzzy matrix games with payoffs of triangular fuzzy numbers," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    • Handle: RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003357
    DOI: 10.1016/j.amc.2024.128874
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324003357
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2024.128874?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. Li, Deng-Feng, 2012. "A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 223(2), pages 421-429.
    2. O. G. Haywood, 1954. "Military Decision and Game Theory," Operations Research, INFORMS, vol. 2(4), pages 365-385, November.
    3. Liu, Yuyuan & Liu, Linjie & Guo, Ruqiang & Zhang, Liang, 2023. "N-player repeated evolutionary trust game under government management," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. Benjamin H. Steven, 1961. "An Application Of Game Theory To A Problem In Location Strategy," Papers in Regional Science, Wiley Blackwell, vol. 7(1), pages 143-157, January.
    5. İzgi, Burhaneddin & Özkaya, Murat & Üre, Nazım Kemal & Perc, Matjaž, 2024. "Matrix norm based hybrid Shapley and iterative methods for the solution of stochastic matrix games," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    6. Sumaila, Ussif Rashid, 1999. "A review of game-theoretic models of fishing," Marine Policy, Elsevier, vol. 23(1), pages 1-10, January.
    7. Lemaire, Jean, 1991. "Cooperative Game Theory and its Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 17-40, April.
    8. İzgi, Burhaneddin & Özkaya, Murat & Üre, Nazım Kemal & Perc, Matjaž, 2023. "Extended matrix norm method: Applications to bimatrix games and convergence results," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    9. Chandra, S. & Aggarwal, A., 2015. "On solving matrix games with pay-offs of triangular fuzzy numbers: Certain observations and generalizations," European Journal of Operational Research, Elsevier, vol. 246(2), pages 575-581.
    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. İzgi, Burhaneddin & Özkaya, Murat & Üre, Nazım Kemal & Perc, Matjaž, 2024. "Matrix norm based hybrid Shapley and iterative methods for the solution of stochastic matrix games," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    2. Chunsheng Cui & Zhongwei Feng & Chunqiao Tan, 2018. "Credibilistic Loss Aversion Nash Equilibrium for Bimatrix Games with Triangular Fuzzy Payoffs," Complexity, Hindawi, vol. 2018, pages 1-16, December.
    3. Deng, Xinyang & Liu, Qi & Deng, Yong, 2016. "Matrix games with payoffs of belief structures," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 868-879.
    4. Suijs, J.P.M. & De Waegenaere, A.M.B. & Borm, P.E.M., 1996. "Stochastic Cooperative Games in Insurance and Reinsurance," Discussion Paper 1996-53, Tilburg University, Center for Economic Research.
    5. Mourdoukoutas, Fotios & Boonen, Tim J. & Koo, Bonsoo & Pantelous, Athanasios A., 2021. "Pricing in a competitive stochastic insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 44-56.
    6. Hutton, Trevor & Sumaila, Ussif Rashid, 2002. "Natural Resource Accounting And South African Fisheries: A Bio-Economic Assessment Of The West Coast Deep-Sea Hake Fishery With Reference To The Optimal Utilisation And Management Of The Resource," Discussion Papers 18018, University of Pretoria, Center for Environmental Economics and Policy in Africa.
    7. Liyuan Lin & Fangda Liu & Jingzhen Liu abd Luyang Yu, 2023. "The optimal reinsurance strategy with price-competition between two reinsurers," Papers 2305.00509, arXiv.org.
    8. Izquierdo, Josep M. & Rafels, Carles, 2001. "Average Monotonic Cooperative Games," Games and Economic Behavior, Elsevier, vol. 36(2), pages 174-192, August.
    9. David M Frank & Sahotra Sarkar, 2010. "Group Decisions in Biodiversity Conservation: Implications from Game Theory," PLOS ONE, Public Library of Science, vol. 5(5), pages 1-10, May.
    10. Jeremy Bulow & Paul Klemperer, 2007. "When are Auctions Best?," Economics Papers 2007-W03, Economics Group, Nuffield College, University of Oxford.
    11. Chunguang Bai & Joseph Sarkis, 2013. "Green information technology strategic justification and evaluation," Information Systems Frontiers, Springer, vol. 15(5), pages 831-847, November.
    12. Kose, Erkan & Erbas, Mehmet & Ersen, Erkan, 2017. "An integrated approach based on game theory and geographical information systems to solve decision problems," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 105-114.
    13. Mongin, Philippe, 2007. "Une étude d'histoire militaire instruite par la Théorie des jeux et quelques amplifications Méthodologiques," HEC Research Papers Series 866, HEC Paris.
    14. Guo, Ruqiang & Liu, Linjie & Liu, Yuyuan & Zhang, Liang, 2024. "Evolution of trust in the N-player trust game with the margin system," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    15. Cui Li & Doudou Wu & Tengfei Shao, 2023. "Research on Sustainable Cooperation Strategies for Cross-Regional Supply Chain Enterprises in Uncertain Environments," Sustainability, MDPI, vol. 15(22), pages 1-31, November.
    16. Jiang, Wenjun & Ren, Jiandong & Yang, Chen & Hong, Hanping, 2019. "On optimal reinsurance treaties in cooperative game under heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 173-184.
    17. Asmussen, Søren & Christensen, Bent Jesper & Thøgersen, Julie, 2019. "Nash equilibrium premium strategies for push–pull competition in a frictional non-life insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 92-100.
    18. Zifeng Zhao & Peng Shi & Xiaoping Feng, 2021. "Knowledge Learning of Insurance Risks Using Dependence Models," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1177-1196, July.
    19. Cano-Berlanga, Sebastián & Giménez-Gómez, José-Manuel & Vilella, Cori, 2017. "Enjoying cooperative games: The R package GameTheory," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 381-393.
    20. Gakushi Ishimura & Sam Herrick & Ussif Sumaila, 2013. "Fishing games under climate variability: transboundary management of Pacific sardine in the California Current System," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 15(2), pages 189-209, April.

    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:apmaco:v:479:y:2024:i:c:s0096300324003357. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.