The research titled “Axioms of Decision Criteria for 3D Matrix Games and Their Applications” led by ITU Mathematics Engineering faculty member Assoc. Prof. Dr. Burhaneddin İzgi was published in Mathematics.
The study focuses on defining characteristic axioms for 3D matrix games and extends 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. They first redefine the Laplace, Wald, Hurwicz, and Savage criteria in 3D. They present a new definition depending on only the ∞-norm of the 3D payoff matrix for the Laplace criterion in 3D. Then, they demonstrate that the Laplace criterion in 3D explicitly satisfies all the proposed axioms, as well as the other three criteria. To the best of their knowledge, this is the first study that brings 3D matrices in decision and game theories together.