AbstractThis paper considers a mixed duopoly two‐sided market of platforms in which a private firm competes with a public firm in a linear city model with fixed demand of full coverage. We examine whether prices of platforms are lower in the mixed duopoly market than in the standard pure duopoly market in which two private firms compete. We show that introducing a public competitor may or may not induce lower prices of the private platform than introducing a private firm, depending on the quality of the public platform service. In particular, if the quality of the public platform is superior, the prices of the platforms are lower than when it competes with the private rival, whereas they are higher if the quality is lower. We also show that the private firm invests more than the public firm. This has the policy implication that maintaining lower platform prices by introducing a competing public platform will not be sustainable in the long run.