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

Murat Özkaya, Burhaneddin İzgi*, Matjaž Perc

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Özet

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.

Orijinal dilİngilizce
Makale numarası4524
DergiMathematics
Hacim10
Basın numarası23
DOI'lar
Yayın durumuYayınlandı - Ara 2022

Bibliyografik not

Publisher Copyright:
© 2022 by the authors.

Finansman

This research was funded by Slovenian Research Agency (grant numbers P1-0403 and J1-2457).

FinansörlerFinansör numarası
Javna Agencija za Raziskovalno Dejavnost RSP1-0403, J1-2457

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