Price war, as an important factor in undercutting competitors and attracting customers, has spurred considerable work that analyzes such conflict situation. However, in most of these studies, quality of service (QoS), as an important decision-making criterion, has been neglected. Furthermore, with the rise of service-oriented architectures, where players may offer different levels of QoS for different prices, more studies are needed to examine the interaction among players within the service hierarchy. In this paper, we present a new approach to modeling price competition in (virtualized) service-oriented architectures, where there are multiple service levels. In our model, brokers, as intermediaries between end-users and service providers, offer different QoS by adapting the service that they obtain from lower-level providers so as to match the demands of their clients to the services of providers. To maximize profit, players, i.e. providers and brokers, at each level compete in a Bertrand game while they offer different QoS. To maintain an oligopoly market, we then describe underlying dynamics which lead to a Bertrand game with price constraints at the providers’ level. We also study cooperation among a subset of brokers. Numerical simulations demonstrate the behavior of brokers and providers and the effect of price competition on their market shares.

Introduction

In today’s highly competitive Internet service market, service providers, in order to survive, should offer their customers more flexibility in both their quality-of-service (QoS) and price offerings, to meet a variety of customer needs and application requirements. Clearly, any successful solution for a service provider to stay in the market, not only depends on supporting new and updated technologies, but also involves economic aspects. However, pricing the services of the network, even without considering quality differentiation, is a challenging problem that involves several issues. There have been many studies that attempted to address these issues with or without considering differentiated QoS. Pricing approaches include Paris Metro Pricing [2], congestion pricing [3,4], rate-reliability pricing [5], and fairness pricing [6]. On the other hand, with the rise of service-oriented architectures, such as computational clouds and recursive networks [7], network virtualization such as CABO [8], and service brokerage companies such as Google’s “Project Fi” [۹], there is a need for more advanced solutions that manage the interactions among service providers at multiple levels. The ultimate goal in service-oriented architectures and network virtualization is to decouple the services offered by network providers from those of service providers which yield the layered structure of the network [10]. Also, brokers as the intermediaries between clients and lower-level providers, play a key role in improving the efficiency of service-oriented structures by matching the demands of clients to the services of providers. They can downgrade or upgrade a service by sharing it among customers or by combining several services to satisfy customers’ demand. For example, in “Project Fi” [۹], Google offers a flat data rate of $10 per gigabyte of data that is provided by either T-Mobile or Sprint, i.e., Google selects the best network provider based on factors such as coverage and performance, thus adding flexibility and providing the best service to its customers. Furthermore, Project Fi customers can manage their costs based on their monthly needs. This is in contrast to network providers, e.g., T-mobile and Sprint, which offer their customers fixed data plans regulated by a static contract.