We are interested in this paper by the competition between MNO and MVNO on a population of heterogeneous customers, with different perceptions of operators offer. The MVNO buys resources from MNO at the wholesale price and offers an added value supposed to be better and at a lower price compared to the incumbent operator. In such a scenario, the rational customer behavior is to choose the virtual operator offer. However, we consider that the market is segmented into two different populations: the first segment is defined by customers attracted by the brand appeal of the MNO as the incumbent operator and the second segment of customers more sensitive to the added value proposed by the MVNO. Thus, the choice of customers will rather depend on their preferences and retail operators offers. We model this problem considering game theory tools and we distinguish three possible situations depending on customers’ preferences. For each situation, we calculate the market share of each of the operators and the Nash equilibrium given by the MNO’s wholesale price and the MVNO’s margin.