Simple Mechanisms for Sequential Capacity Allocations

We consider a sequential capacity allocation problem of a firm to its retail branches that sell the firm's product. The orders of the retail branches to the headquarters arrive sequentially, and each allocation decision has to be made before the next order arrives. The objective of the headquarters is to maximize the overall firm profit, that is, the total profit of all the retail branches. Each retail branch makes ordering decision independently by using private information about its local market condition in order to maximize its own profit. Hence, they may strategically inflate their order quantities in their favor, potentially hurting the firm profit. We first discuss the importance of capacity rationing in maximizing the firm's profit by finding the first-best allocation outcome, the optimal solution without information asymmetry. Based on this, we design mechanisms that effectively overcome the information asymmetry. First, we design a simple threshold-type mechanism where truthful reporting is optimal and capacity rationing is implemented by limiting allocation beyond a pre-specified threshold. We show this mechanism is optimal within the class of mechanisms that do not allow any side payments. We also design a mechanism with side payments that is optimal among all possible mechanisms. In particular, we show that this payment-based mechanism achieves the first-best allocation, fully overcoming information asymmetry. Although optimal, it may not be practical because of the complexity in the side payment menu, so we also propose a simple variant of it with only a few parameters. Our extensive numerical study shows that our simple threshold-type and payment-based mechanisms achieve near-optimal performance.