Stackelberg Mean-Field Games for Adaptive Cancer Therapy

We propose a Stackelberg mean-field game for adaptive cancer therapy, coupling a clinician's dosing problem to a tumor mean-field equilibrium described by Hamilton--Jacobi--Bellman and Fokker--Planck equations. Under a monotonicity condition on competition we prove existence of equilibria, derive Stackelberg optimality conditions, and obtain an $O(N^{-1/2})$ finite-player limit; a finite-type reduction yields a tractable ODE model. Numerical experiments show that S-MFG-optimal schedules significantly outperform maximum tolerated dose and heuristic adaptive policies in delaying resistance emergence while using less drug.