Merger paradox from industrial organization: I believe a fairly good overview is here: Garcia, F, Paz y Miño, JM, Torrens, G. The merger paradox, collusion, and competition policy. J Public Econ Theory. 2020; 22: 2051– 2081. https://doi.org/10.1111/jpet.12448.
You can find a fair deal about it here as well: R. Rothschild, John S. Heywood, Kristen Monaco, Spatial price discrimination and the merger paradox, Regional Science and Urban Economics, Volume 30, Issue 5,
2000, Pages 491-506 https://doi.org/10.1016/S0166-0462(00)00044-2
The general overview of this paradox is that it is unclear, under traditional models, why one firm would bother to purchase another. If they do so, the only point is to cut total overall production. But the sale price of any such firm will (under most conditions) be prohibitively expensive. Furthermore, the firms that are excluded from this merger benefit from reduced production - and they didn't have to bother to buy anyone. Some solutions include assuming extremely concave production functions, sticky/immobile customers distributed along some preference space, and others.
Previously, IO had an unsolved mystery of how firms chose to enter sequentially in spatially price-discriminating markets for the n-firm case in linear markets and circular markets. I know circular markets have been solved, and I think linear markets have also been solved recently.
