Robust Dynamic Pricing and Admission Control with Fairness Guarantees

Abstract

Dynamic pricing is commonly used to regulate congestion in shared service systems. This paper is motivated by the fact that in the presence of users with varying price sensitivity (responsiveness), conventional monotonic pricing can lead to unfair outcomes by disproportionately excluding price-elastic users, particularly under high or uncertain demand. We therefore develop a fairness-oriented mechanism under demand uncertainty. The paper's contributions are twofold. First, we show that when fairness is imposed as a hard state constraint, the optimal (revenue maximizing) pricing policy is generally non-monotonic in demand. This structural result departs fundamentally from standard surge pricing rules and reveals that price reduction under heavy load may be necessary to maintain equitable access. Second, we address the problem that price elasticity among heterogeneous users is unobservable. To solve it, we develop a robust dynamic pricing and admission control framework that enforces capacity and fairness constraints for all user type distributions consistent with aggregate measurements. By integrating integral High Order Control Barrier Functions (iHOCBFs) with a robust optimization framework under uncertain user-type distribution, we obtain a controller that guarantees forward invariance of safety and fairness constraints while optimizing revenue. Numerical experiments demonstrate improved fairness and revenue performance relative to monotonic surge pricing policies.