We study the tessellation defined as the intersection of two independent planar Poisson-Voronoi tessellations and derive the means of its main geometrical characteristics. For this intersection tessellation, we distinguis- h between six types of cells depending on whether they contain the nuclei of the two initial tessellations or not. The intensity and the mean area of each type of cell are computed either in closed form or via asymptotic expansions. The model can be used to represent the local zones of two competing telecommunication operators. Then the interconnection of two subscribers induces a specific cost within each type of cell of the intersecti- on tessellation associated with the two systems of local zones.