Finding the Maxmin of constructive entries in arbitrary game theory 
matrices

Matthew Chin; Huiling Jin; Hannah Liu; Zimu Wang

doi:10.1117/12.2628231

22 April 2022 Finding the Maxmin of constructive entries in arbitrary game theory matrices

Matthew Chin, Huiling Jin, Hannah Liu, Zimu Wang

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 1216341 (2022) https://doi.org/10.1117/12.2628231
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

We construct a 1 x 2 matrix (a_n, b_n), 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.

Citation Download Citation

Matthew Chin, Huiling Jin, Hannah Liu, and Zimu Wang "Finding the Maxmin of constructive entries in arbitrary game theory matrices", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 1216341 (22 April 2022); https://doi.org/10.1117/12.2628231

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