Pricing Demand-Side Flexibility via Mean-Field Reverse Stackelberg Game

Pricing demand-side flexibility is crucial for incentivizing real-time adjustments in energy consumption, balancing grid supply and demand, and accelerating the integration of renewable resources. However, designing effective pricing mechanisms to guide large-scale consumers toward desired load profiles remains a significant challenge. This paper introduces a mean-field reverse Stackelberg game framework to model strategic interactions between a load aggregator and a population of consumers. The aggregator, acting as the leader, designs an affine pricing scheme to align aggregated demand with a target load profile, while consumers, as followers, optimize their demand response to maximize individual utility. To address computational intractability in large-scale settings, we employ a mean-field game to characterize consumer equilibrium behavior and demonstrate that the mean-field equilibrium serves as a precise approximation of the equilibrium arising from consumer interactions. We further propose efficient algorithms for computing both the mean-field equilibrium and optimal pricing policies. Numerical studies show that our reverse Stackelberg game-based pricing scheme effectively flattens both the demand curve and retail prices. This demonstrates the success of the proposed RSG-based pricing strategy in achieving peak shaving and valley filling, thereby improving the management of large-scale consumer demand in smart grids.