| Title: | Axioms of decision criteria for 3D matrix games and their applications |
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| Authors: | ID Özkaya, Murat (Author)
ID İzgi, Burhaneddin (Author)
ID Perc, Matjaž (Author) |
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| Files: |  Ozkaya-2022-Axioms_of_Decision_Criteria_for_3D.pdf (474,80 KB)
MD5: 6EAD0EC3CCAA147C74F6B94E0524A4F8
 https://doi.org/10.3390/math10234524
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| 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. |
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| Keywords: | game theory, decision criteria, matrix game, common goods, characteristic axioms, multi-state games, three-dimensional matrix games, game against nature, COVID-19, insurance problem |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 10.10.2022 |
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| Article acceptance date: | 23.11.2022 |
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| Publication date: | 30.11.2022 |
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| Publisher: | MDPI |
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| Year of publishing: | 2022 |
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| Number of pages: | Str. 1-20 |
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| Numbering: | Letn. 10, Št. 23, št. članka 4524 |
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| PID: | 20.500.12556/DKUM-88777  |
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| UDC: | 53 |
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| ISSN on article: | 2227-7390 |
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| COBISS.SI-ID: | 131992835 |
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| DOI: | 10.3390/math10234524 |
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| Publication date in DKUM: | 27.05.2024 |
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| Views: | 395 |
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| Downloads: | 17 |
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| Metadata: |    |
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| Categories: | Misc.
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