Finding the Maxmin of constructive entries in arbitrary game theory matrices
Matthew Chin, Huiling Jin, Hannah Liu, Zimu Wang · International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021) · 2022
We construct a 1 x 2 matrix (an, bn), whose entries are constructive real numbers. We demonstrate that the values of the minmax and maximin of any matrix can be algorithmically determined. In the second part of the paper, we will show through proof by contradiction that there does not exist a program that can find the coordinates of the maximin or the minmax. Together, these form a proof of the fact that every matrix with constructive entries has a maxmin, but that it is not possible to construct a program that given an arbitrary matrix tells the coordinates of the maxmin.