Efficiency of Stable Matching with Two-Sided Incomplete Information

We study a two-sided job market matching setting with transferable utilities and incomplete information on both sides. We propose a definition of stable matching with two-sided incomplete information. Assume that the workers and firms' premuneration values in a match are strictly monotonic and strictly supermodular in their types; moreover, all of them have common knowledge that the wage is strictly increasing in their types. We show that every stable matching outcome is efficient.