A fast optimization approach for seeking Nash equilibrium based on Nikaido–Isoda function, state transition algorithm and Gauss–Seidel technique

Abstract

This paper proposes a fast optimization approach for non-cooperative games with complicated payoff functions (non-smooth, non-concave, etc.). The Nikaido–Isoda function is employed to convert knotty Nash equilibrium problems (NEPs) into large-scale optimization problems with complex objective functions. To efficiently seek Nash equilibrium, the resulting optimization problems are decomposed into many subproblems where each player tries to maximize its payoff when observing others’ current strategies. All players’ strategies are updated iteratively until reaching Nash equilibrium. Specifically, a dynamic state transition algorithm (STA) is proposed to seek global optima of subproblems at each iteration, and the sequential quadratic programming (SQP) is embedded into dynamic STA for convergence acceleration. A Gauss–Seidel technique is utilized for players’ strategy updates to improve computational efficiency further. Numerical examples drawn from multidisciplinary contexts validate that the proposed approach could effectively seek out Nash equilibrium for simultaneously decreasing the time-consuming remarkably.