Notes on excess entry theorem in a Kantian oligopoly

This study revisits the excess entry theorem for quantity and price competition with substitutes and complements in a Kantian oligopoly. In such an oligopoly, we demonstrate that the equilibrium market outcomes are the same between the aforementioned two types of competition regimes with substitutes and complements, and in particular, each firm's equilibrium price and consumer surplus do not depend on the number of firms. Therefore, in quantity and price competition with substitutes and complements in a Kantian oligopoly, the excess entry theorem holds that the number of firms is larger under free entry than under the second-best social optimality. Finally, in the two types of competition with substitutes and complements, we characterize the ranking orders of the number of firms between free entry and the second-best social optimality in Kantian and Nashian oligopolies.