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

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dc.authoridOzkaya, Murat/0000-0001-7241-4710
dc.authoridPerc, Matjaz/0000-0002-3087-541X
dc.authoridFerreira, Manuel Alberto M./0000-0002-4931-3281
dc.contributor.authorOzkaya, Murat
dc.contributor.authorIzgi, Burhaneddin
dc.contributor.authorPerc, Matjaz
dc.date.accessioned2025-01-27T21:03:55Z
dc.date.available2025-01-27T21:03:55Z
dc.date.issued2022
dc.departmentÇanakkale Onsekiz Mart Üniversitesi
dc.description.abstractIn 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 infinity-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.
dc.identifier.doi10.3390/math10234524
dc.identifier.issn2227-7390
dc.identifier.issue23
dc.identifier.scopus2-s2.0-85143634236
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.3390/math10234524
dc.identifier.urihttps://hdl.handle.net/20.500.12428/27493
dc.identifier.volume10
dc.identifier.wosWOS:000896245600001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofMathematics
dc.relation.publicationcategoryinfo:eu-repo/semantics/openAccess
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20250125
dc.subjectcharacteristic axioms
dc.subjectmulti-state games
dc.subjectthree-dimensional matrix games
dc.subjectgame against nature
dc.subjectCOVID-19
dc.subjectinsurance problem
dc.titleAxioms of Decision Criteria for 3D Matrix Games and Their Applications
dc.typeArticle

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