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.