Robust Dynamic Pricing and Admission Control with Fairness Guarantees
This addresses fairness and efficiency issues in congestion management for shared service systems like ride-sharing or cloud computing, offering a novel approach with practical implications.
The paper tackles the problem of unfair exclusion of price-elastic users in dynamic pricing systems under heterogeneous user groups and uncertain demand, showing that optimal pricing is non-monotonic and developing a robust framework that improves fairness and revenue compared to monotonic surge pricing.
Dynamic pricing is commonly used to regulate congestion in shared service systems. This paper is motivated by the fact that when heterogeneaous user groups (in terms of price responsiveness) are present, conventional monotonic pricing can lead to unfair outcomes by disproportionately excluding price-elastic users, particularly under high or uncertain demand. 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 resource capacity and fairness constraints for all user type distributions consistent with aggregate measurements. By integrating integral High Order Control Barrier Functions (iHOCBFs) with a worst case robust optimization framework, 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.