A Novel Elitism-Based Genetic Algorithm with Gradient-Based Local Search for Seeking Local Nash Equilibrium in Non-Cooperative Game

Abstract

The purpose of analyzing non-cooperative game problems is to find the equilibrium point that all players reach according to the game rules, namely the Nash Equilibrium (NE). As a broader equilibrium concept that includes NE, local NE (LNE) also deserves attention for its similar stability to NE, as the NE is usually hard to obtain. This paper proposes a novel paradigm to game theory, which very first applies the idea of evolutionary computation to find the LNE in a non-cooperative game. This study transforms the abstract definition of LNE into an optimization problem with a concrete objective function and proposes a novel elite genetic algorithm (EGA) to effectively seek the LNE in non-cooperative games. In the aspect of algorithm designing, EGA adopts an elite strategy to retain the most promising individuals and incorporates gradient descent for local search to enhance the genetic algorithm’s local search capability. The performance of EGA is evaluated in extensive test cases of small-scale 5-player games, large-scale games, and complex game scenarios. The experimental results demonstrate the effectiveness and efficiency of EGA in finding the LNE. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.