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Axioms of Decision Criteria for 3D Matrix Games and Their Applications

Author

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  • Murat Özkaya

    (Department of Mathematics, Istanbul Technical University, Istanbul 34469, Turkey
    Departmant of Business, Çanakkale Onsekiz Mart University, Çanakkale 17100, Turkey)

  • Burhaneddin İzgi

    (Department of Mathematics, Istanbul Technical University, Istanbul 34469, Turkey)

  • Matjaž Perc

    (Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, 2000 Maribor, Slovenia
    Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan
    Alma Mater Europaea, Slovenska Ulica 17, 2000 Maribor, Slovenia)

Abstract

In this paper, we define characteristic axioms for 3D matrix games and extend the definitions of the decision criteria under uncertainty to three dimensions in order to investigate the simultaneous effect of two different states on the decision process. We first redefine the Laplace, Wald, Hurwicz, and Savage criteria in 3D. We present a new definition depending on only the ∞ -norm of the 3D payoff matrix for the Laplace criterion in 3D. Then, we demonstrate that the Laplace criterion in 3D explicitly satisfies all the proposed axioms, as well as the other three criteria. Moreover, we illustrate a fundamental example for a three-dimensional matrix with 3D figures and show the usage of each criterion in detail. In the second example, we model a decision process during the COVID-19 pandemic for South Korea to show the applicability of the 3D decision criteria using real data with two different states of nature for individuals’ actions for the quarantine. Additionally, we present an agricultural insurance problem and analyze the effects of the hailstorm and different speeds of wind on the harvest by the 3D criteria. To the best of our knowledge, this is the first study that brings 3D matrices in decision and game theories together.

Suggested Citation

  • Murat Özkaya & Burhaneddin İzgi & Matjaž Perc, 2022. "Axioms of Decision Criteria for 3D Matrix Games and Their Applications," Mathematics, MDPI, vol. 10(23), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4524-:d:989063
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    References listed on IDEAS

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    1. Walker, Linus & Hischier, Illias & Schlueter, Arno, 2022. "Scenario-based robustness assessment of building system life cycle performance," Applied Energy, Elsevier, vol. 311(C).
    2. Ballestero, E. & Gunther, M. & Pla-Santamaria, D. & Stummer, C., 2007. "Portfolio selection under strict uncertainty: A multi-criteria methodology and its application to the Frankfurt and Vienna Stock Exchanges," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1476-1487, September.
    3. Alex Bennet & David Bennet, 2008. "The Decision-Making Process in a Complex Situation," International Handbooks on Information Systems, in: Handbook on Decision Support Systems 1, chapter 1, pages 3-20, Springer.
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    Cited by:

    1. Teng-Chiao Lin & Hsing-Hui Chen & Kuen-Suan Chen & Yen-Po Chen & Shao-Hsun Chang, 2023. "Decision-Making Model of Performance Evaluation Matrix Based on Upper Confidence Limits," Mathematics, MDPI, vol. 11(16), pages 1-11, August.

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