About a dilemma in the telecommunications sector: Virtual operators or low-cost operators?

A virtual operator is fragile when it is in competition with other virtual operators. This is explained by the “Bertrand paradox”: when firms sell products not differentiated (or not enough differentiated) a price war has terrible consequences (the profits tend to zero). But it is worse if there is a price war between the operators with a network. It occurred in France during the period 2012 – 2018. The entrant Free triggered a price war. The reaction of the incumbents was to create low-cost operators which were their branches. The only virtual operator with a large size, Virgin Mobile, was “bought and closed down” by the incumbent SFR. It suffered too much because of the incumbents decreasing their prices and the low-cost operators, both. It lost many customers. One proposes a model to explain why the “buy and close down” of Virgin Mobile was profitable (and chosen) in these conditions. The method used is Bertrand competition. Also, the “buy and close down” which is profitable is a criterium for products which are not enough differentiated. A few examples are given. The aims of the paper are two: - To study how works a price war in telecommunications. - More generally, the possibility of profitable “buy and close down” allows to propose a criterium for saturated markets. Even, the criterium could be used to build software (to test if a market is saturated or not). The rival models which are presented in the literature are commente