20.500.12556/DKUM-88777 Axioms of decision criteria for 3D matrix games and their applications 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. game theory decision criteria matrix game common goods characteristic axioms multi-state games three-dimensional matrix games game against nature COVID-19 insurance problem teorija iger odločitveni kriteriji matrična igra skupno dobro tridimenzionalne matrične igre igra proti naravi problem zavarovanja true true true MDPI Angleški jezik Slovenski jezik Znanstveno delo 2024-05-24 03:58:02 2024-05-27 13:50:29 2024-07-16 03:58:11 0000-00-00 00:00:00 2022 0 0 Str. 1-20 Št. 23, št. članka 4524 Letn. 10 2022 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2022-10-10 2022-11-23 2022-11-30 53 131992835 10.3390/math10234524 2227-7390 Ozkaya-2022-Axioms_of_Decision_Criteria_for_3D.pdf Ozkaya-2022-Axioms_of_Decision_Criteria_for_3D.pdf 1 6EAD0EC3CCAA147C74F6B94E0524A4F8 aeab3de4862a98d0a58a3689a18109ab05627a5e9f2e99abeb00b604a023298a 3e124def-42a1-11ef-99b3-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=181489 https://doi.org/10.3390/math10234524 0 4b5b7991-42a1-11ef-99b3-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=181490 Fakulteta za naravoslovje in matematiko 0 0 0