Bertrand-Edgeworth pricing equilibrium in Web service markets

PricingWebserviceswithdifferentQualityofService(QoS)classesovertheInternetisachallengingscientificproblem. 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.

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