Admission Control Game with Capacity Borrowing

We study a decentralized admission control problem with capacity borrowing. In this problem, the admission decision is made by each server who is assigned dedicated capacity. However, a server can borrow capacity from other servers if his dedicated capacity is exhausted. The borrower compensates the lender by a payment equal to the “borrowing cost.” Hence, the servers share their capacities via borrowing, but they also compete against each other for their pooled capacities. We formulate this problem as a stochastic dynamic game and characterize the equilibrium strategic admission behavior of servers. We show that the critical factors that affect the equilibrium behavior and the system revenue are the magnitude of the borrowing cost, the arrival rate of customers and the revenue difference between different classes of customers. We have identified conditions under which servers maximizing their own payoffs end up making decisions that benefit the system. Our study highlights the important roles that the borrowing cost plays in shaping servers’ behavior in service systems and provides concrete guidance for practitioners to design a decentralized admission control system.