The Stackelberg–Armstrong model

Abstract

We show that sequential (Stackelberg) competition between two-sided platforms can overturn the price-skewness ranking of the Armstrong (2006) competition benchmark: the side subsidized under simultaneous pricing may become the taxed side under sequential play. The mechanism is that the Stackelberg leader internalizes cross-side feedback through the follower’s best response, which introduces both externalities into each side’s markup and can reverse which side is subsidized. The equilibrium is unique, admits closed-form solutions under standard interiority/concavity conditions, and is directly comparable to Armstrong’s benchmark. Both platforms earn strictly more than under simultaneous play, and we characterize a sharp threshold separating second-mover from first-mover advantage.