Abstract. We study the implementation of constrained‐efficient allocations in labour markets where a basic coordination problem leads to an equilibrium matching friction. We argue that these allocations can be achieved in a non‐cooperative equilibrium if wages are determined by ex post bidding. This holds true even in finite‐sized markets where the equilibrium‐matching process has decreasing returns to scale – where the ‘Hosios rule’ does not apply – both with and without heterogeneity. JEL classification: D83, J64