We consider a system in which two competing servers provide customer-intensive services and the service reward is affected by the length of service time. The customers are boundedly rational and choose their service providers according to a logit model. We demonstrate that the service provider revenue function is unimodal in the service rate, its decision variable, and show that the service rate competition has a unique and stable equilibrium. We then study the price decision under three scenarios with the price determined by a revenue-maximizing firm, a welfare-maximizing social planner, or two servers in competition. We find that the socially optimal price, subject to the requirement that the customer actual utility must be non-negative, is always lower than the competition equilibrium price which, in turn, is lower than the revenue-maximizing monopoly price. However, if the customer actual utility is allowed to be negative in social optimization, the socially optimal price can be higher than the other two prices in a large market.