Bertrand-Edgeworth pricing equilibrium in Web service markets

Pricing Web services with different Quality of Service (QoS) classes over the Internet is a challenging scientific problem. Finding the optimal price per QoS class allows each provider to maximize its revenue and to solve the capacity planning problem. The most works presented in the literature focus on a monopolistic setting where one service provider sells one or more services of different classes to a number of customers. The Service Level Agreement (SLA) is the most commonly used contract scheme, whereby providers announce their QoS profiles specifying a number of QoS classes and the related prices. The most results available in the literature to find the optimal QoS profile of a provider do not take into account the QoS profiles announced by other providers. However, in real–world settings, services sale competition among service providers is common and cannot be neglected. In this paper, we design a game–theoretical model for Web service markets with a single service characterized by response time and price by extending the Bertrand–Edgeworth’s oligopoly, and we provide a polynomial–time algorithm to find a Nash equilibrium with two providers and an arbitrary number of customers.