In this paper, we tackle the dilemma of pruning versus proliferation in a vertically differentiated oligopoly under the assumption that some firms collude and control both the range of variants for sale and their corresponding prices, likewise a multiproduct firm. We analyse whether pruning emerges and, if so, a fighting brand is marketed. We find that it is always more profitable for colluding firms to adopt a pricing strategy such that some variants are withdrawn from the market. Under pruning, these firms commercialize a fighting brand only when facing competitors in a low-end market.
Jaskold Gabszewicz, J., Marini, M. A., & Tarola, O. (2017). Vertical differentiation and collusion: pruning or proliferation? Research in Economics, 71(1), 129-139. https://doi.org/10.1016/j.rie.2016.10.003 (Original work published 2017)