Price war with migrating customers

In the telecommunication world, competition among providers to attract and keep customers is fierce. On the other hand customers churn between providers due to better prices, better reputation or better services. We propose in this paper to study the price war between two providers in the case where users' decisions are modeled by a Markov chain, with price-dependent transition rates. Each provider is assumed to look for a maximized revenue, which depends on the strategy of the competitor. Therefore, using the framework of non-cooperative game theory, we show how the price war can be analyzed and show the influence of various parameters.