A Nash-Stackelberg Game Equilibrium Approach for Electricity Markets Using RBF-Based Value Function Approximation

With deepening power market reforms and dual carbon policies, the coupling between electricity and carbon markets has intensified, creating complex multi-agent decisionmaking environments. Under this background, building a multi-agent bidding strategy model and efficiently solving it become crucial. This paper constructs a bi-level Nash-Stackelberg game model for multi-agent bidding in coupled electricity-carbon markets and proposes a Nash-Stackelberg game optimization algorithm based on value function approximation. We design an improved inverse quadratic kernel Radial Basis Function (RBF) approximation value function to characterize the electricity market’s influence on agent decisions. In this way, the bi-level game can be transformed into a single-level Nash game, thereby reducing the computational burden. The proposed approach exhibits a relative error of 1.311% and a computation time of 58.43 seconds in the IEEE 6-bus system, which outperform classical Karush-Kuhn-Tucker (KKT) and Particle Swarm Optimization (PSO)methods. These results indicate that. The proposed approach significantly reduces computational complexity while maintaining high accuracy.