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.
Jaskold Gabszewicz, J., Marini, M. A., & Tarola, O. (2016). Core existence in vertically differentiated markets. Economics Letters, 149, 28-32. https://doi.org/10.1016/j.econlet.2016.09.032 (Original work published 2016)