Robust design in monotonic matching markets: A case for firm-proposing deferred-acceptance

We study two-sided matching markets among workers and firms. Workers seek one position at a firm but firms may employ several workers. In many applications those markets are monotonic: leaving positions unfilled is costly as for instance, for hospitals this means not being able to provide full service to its patients. A huge literature has advocated the use of stable mechanisms for clearinghouses. The interests among workers and firms are polarized among stable mechanisms, most famously the firm-proposing DA and the worker-proposing DA. We show that for the firm-proposing DA ex-ante incentive compatibility and ex-post incentive compatibility are equivalent whereas this is not necessarily true for the worker-proposing DA. The firm-proposing DA turns out to be more robust than the worker-proposing DA under incomplete information when incentives of both sides of the market are important.