Matching Markets under (In)complete Information

We are the first to introduce incomplete information to centralized many-to-one matching markets such as those to entry-level labor markets or college admissions. This is important because in real life markets (i) any agent is uncertain about the other agents' true preferences and (ii) most entry-level matching is many-to-one (and not one-to-one). We show that for stable (matching) mechanisms there is a strong and surprising link between Nash equilibria under complete information and Bayesian Nash equilibria under incomplete information. That is,given a common belief, a strategy profile is a Bayesian Nash equilibrium under incomplete information in a stable mechanism if and only if, for any true profile in the support of the common belief, the submitted profile is a Nash equilibrium under complete information at the true profile in the direct preference revelation game induced by the stable mechanism. This result may help to explain the success of stable mechanisms in these markets.