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

We consider a service system with two competing firms offering service via different pricing and service rules. With the fixed-price firm, customers obtain service at a fixed price, and have homogeneous expected waiting times. With the bid-based firm, customers submit a bid to obtain service, and incur expected waiting times decreasing in their bids, and pay their bids. We assume the customers are heterogeneous, with different waiting costs, and choose the firm from which to obtain service strategically on arrival. We establish the existence and uniqueness of a symmetric equilibrium for the customers' decision problem for any given fixed and reserve price set by the two firms, and characterize the structure of the resulting equilibrium strategy. In particular, we show that the customers' equilibrium strategy has a simple threshold structure, where customers with either high or low waiting cost choose to obtain service from the bid-based firm, whereas those with moderate waiting cost choose the fixed-price firm. We use this characterization of the equilibrium strategy to study the price competition between the two firms in a limiting regime where the customer arrival rate and the service capacities increase proportionally, and show that the total expected revenue of the two competing firms is comparable to that under collusion