Wireless users have the opportunity to choose between heterogeneous access modes, such as 3G, WiFi or WiMAX for instance, which operate with different distance ranges. Due to the increasing commercial interest in access networks, those technologies are often managed by competing providers. The goal of this paper is to study the price war occuring in the case of two providers, with one provider operating in a sub-area of the other. A typical example is that of a WiFi operator against a WiMAX one, WiFi being operated in the smaller area. Using a simple model, we discuss how, for fixed prices, (elastic) demand is split among providers, and then characterize the Nash equilibria for the price war. We derive the conditions on provider capacities and coverage areas under which providers share demand on the common area. A striking additional result is that among the Nash equilibria, the one for which providers set the largest price corresponds to the case when the competitive environment does not bring any loss in terms of social welfare with respect to the socially optimal situation: at equilibrium, the overall utility of the system is maximized. The price of stability is one.