A Reduced-Order Framework for Stochastic Mean-Field Incentive Stackelberg Games with Delays and Its Application to CACC Platoons

Abstract

This paper investigates approximate strategies for stochastic mean-field incentive Stackelberg games with time delays. In this framework, a leader designs an incentive mechanism to steer noncooperative followers-who act according to a Nash equilibrium-toward the team-optimal solution. Compared with existing studies, we establish new sufficient solvability conditions via a coupled high-dimensional Lyapunov-type equations (CHLEs). To overcome the computational intractability that arises as the population size grows, we develop a reduced-order approach exploiting the asymptotic structure of the CHLEs. Based on this structure, we construct a population-size-independent approximate strategy and we quantify its near-optimality in terms of the associated cost function. The proposed framework is validated through numerical simulations of a connected and automated vehicle (CAV) platoon under stochastic disturbances, sensing noise, network latency, and actuation delay. The results confirm that the reduced-order strategy accurately captures the dominant closed-loop behavior of the full-order solution, demonstrating both scalability and practical effectiveness of the proposed method.