Coordinating incentives and curb capacity in a food delivery platform

This paper develops an analytical framework linking platform incentives and curb capacity in food delivery systems. A restaurant serves dine-in, pickup, and delivery customers who share limited curb or parking space, while the platform sets commissions and a per-delivery wage that governs driver availability. The restaurant responds by setting menu prices, investing in total curb capacity, and allocating it across service channels. Customer demand follows a spatial Hotelling structure, and waiting times arise endogenously from congestion that increases with channel load and decreases with allocated capacity. Delivery throughput is constrained by a concave driver-supply function. The Stackelberg interaction between the platform and the restaurant is formulated as a mathematical program with equilibrium constraints. We give conditions for existence and uniqueness of equilibrium. Results show two operating regimes as follows. When drivers are scarce, delivery is priced at a choke level that exactly fills driver capacity. Higher wages increase driver-supply and lower the choke price, while higher commissions raise it. When drivers are abundant, delivery behaves as a regular differentiated channel and the optimal wage collapses to a minimum. Optimal curb capacity equalizes its marginal cost with the congestion-relief benefit propagated through demand, decreasing with higher commissions and increasing with higher wages. The results reveal that incentives (commissions and wages) and physical investments (curb capacity) are strategic complements. Providing better pay when drivers are scarce and lowering commissions when curb expansion is needed together lead to higher throughput, shorter waits, and greater overall profit.