Core existence in vertically differentiated markets

•We provide a sufficient condition for the existence of core in a vertically differentiated oligopoly.•The condition required is the equidistance of all products along the quality space.•We show that, when this regularity condition is relaxed, the core can be easily empty.

We prove that a sufficient condition for the core existence in a n-firm vertically differentiated market is that the qualities of firms' products are equispaced along the quality spectrum. This result contributes to see that a fully collusive agreement among firms in such markets is more easily reachable when product qualities are not distributed too asymmetrically along the quality ladder.