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.