Joint Price and QoS Market Share Game with Adversarial Service Providers and Migrating Customers

In order to attract more and more customers, the price war between service providers (SPs) is becoming increasingly fierce. This kind of conflict situations has been analyzed and hugely studied by a plenty of works in the related literature. However unfortunately, almost all prior works neglect an important decision parameter, it is the promised quality of service which can be a serious advantage to register to an operator rather than the others. In this paper, we formulate the interaction between service providers as a non-cooperative game. First, each SP chooses the Quality of Service (QoS) to guarantee (it depends on the amount of requested bandwidth) and the corresponding price. Second, the customers decide to which SP to subscribe defining the market share for each SP. Then, each customers may migrate/churn to another SP or alternatively switch to “no subscription state” depending on the observed price/QoS. Furthermore, we build a Markovian model to derive the behaviour of customers depending on the strategic actions of the SPs. Finally, we provide extensive numerical examples to show the importance of taking price and QoS as a joint decision parameters and provide thereby some insights/heuristic on how to set them.