Irmen and Thisse (1998) demonstrate that two firms competing with multicharacteristic products differentiate them in one characteristic completely, while keeping them identical in all others. This paper shows that their min-…-min-max differentiation result is not robust with respect to the number of firms. A market setting that replicates their result in a duopoly, but fails to do so in a three firm oligopoly is identified. Symmetric pure strategy equilibrium with three firms differentiating their products in two dimensions, but not completely in either of them, is a novel medium-medium differentiation result.
Feldin, A. (2012). Three firms on a unit disk market: intermediate product differentiation. Economic and Business Review, 14(4). https://doi.org/10.15458/2335-4216.1236