Ex post bidding and efficient coordination unemployment

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.