High-Dimensional Nash Equilibria Problems and Tensors Applications

Abstract

We propose, in this work, an overview on tensors application in game theory, and basically on Nash equilibria problems. In this paper, we extend the classic normal form of a game to a new form called Tensor form. We present some tensors concepts and operations with detailed examples and then we propose an efficient methodology to solve pure and mixed high-dimensional Nash equilibria problems using tensors operations. The efficiency of this methodology is shown in numerical examples for pure and mixed strategy. An algorithm based on tensors is also implemented to describe and solve these problems.