Bilateral trading with incomplete information and price convergence in a small market: The continuous support case

Chatterjee and Das (2017) recently examined a model of a small market with two homogeneous buyers and two heterogeneous sellers with one of the sellers having private information. They show that as agents become patient enough, for any prior belief about the type of the privately informed seller, in any stationary equilibrium, prices in all transactions converge to the highest possible valuation of the informed seller. In the model, it was assumed that the privately informed seller's type is distributed on a two-point support. In this note, we argue that the asymptotic uniqueness result also holds when the privately informed seller's valuation is distributed on a continuous support. This shows the robustness of the uniqueness result obtained in Chatterjee and Das (2017).