Predicting Nash Equilibria in Bimatrix Games Using a Robust Bichannel Convolutional Neural Network

In this article, we consider the problem of finding a Nash equilibrium in bimatrix games. Traditional solution methods, including the Lemke-Howson (LH) algorithm and enumeration methods, rely on iterative approaches, which leads to computational inefficiency, especially when dealing with multiple instances. To address this problem, we introduce a bichannel convolutional neural network (BiCNN) that receives a bimatrix game as an input and generates two mixed strategies as a predicted Nash equilibrium. To improve the robustness of the BiCNN model, we propose a novel training algorithm that uses bimatrix games generated from different game sizes and probability distributions. Finally, our experimental results show that the proposed approach offers a significant computational advantage while maintaining acceptable prediction accuracy. © 2020 IEEE.