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Many service systems offer multiple modes of service, where each mode differs in price as well as the priority of service. We consider a service system where service is offered via two modes. In the first mode, customers obtain service at a fixed price, and the service discipline is first-in-first-out (FIFO). In the second mode, referred to as the bid-based priority mode, customers submit a bid to obtain service, get serviced in the descending order of their bids, and make payments equal to their bids. We assume the customers are heterogeneous, with different waiting costs, and choose the mode of service strategically on arrival. We establish the existence and uniqueness of a symmetric equilibrium, and characterize the structure of the equilibrium strategy. In particular, we show that the equilibrium strategy has a simple threshold structure, where customers with either high or low waiting cost choose to obtain service from the bid-based priority mode, whereas those with moderate waiting cost choose to obtain service from the FIFO mode. We use the equilibrium characterization to numerically study the service provider’s revenue. In particular, we numerically explore conditions under which operating a dual-mode system may generate more revenue than a bid-based priority mode with optimal reserve price.

When Fixed Price Meets Priority Auctions: Competing Firms with Different Pricing and Service Rules