Web services have become quite popular over the last few years as they allow easier development and integration of business applications. In this paper, we consider a web service pricing problem where two providers compete through dynamic pricing. Each provider offers access to a web service with different quality classes where users may buy their required web service through a reservation system. They would like to adjust the prices of their web services over a pre-specified time horizon to manage demand and to maximize profit. Users have the right with no obligation to cancel their services as long as they pay a penalty. We consider a dynamic setting where the web service classes share a capacity. We first develop a time continuous model for competitive pricing of a web service and then we provide some insights about the equilibrium condition of the problem using open-loop differential game and propose an algorithm to obtain the optimal pricing policy for providers. Moreover, we conduct numerical analyses to examine the impacts of some parameters on control and state variables.