Matching Under Preference Uncertainty: Random Allocation, Informativeness, and Welfare

TL;DR

This paper explores a matching market with uncertain preferences, proposing probabilistic offers to achieve stability and market clearing, while analyzing how information affects applicant welfare.

Contribution

It introduces probabilistic offers in matching markets to handle preference uncertainty and examines their impact on stability and welfare.

Findings

Probabilistic offers enable ex-ante market clearing.

More information can sometimes worsen applicant welfare.

The approach balances stability with informational challenges.

Abstract

This paper studies a decentralized many-to-one matching market where preferences remain uncertain during the matching process. Institutions initiate matching by sending offers, and applicants decide whether to accept upon receiving them. Since applicants learn their preferences only after receiving offers, institutions face a challenge in deciding how many offers to issue. I address this challenge by introducing probabilistic offers (admitting applicants with a probability less than one), which ensure that ex-ante market clearing and stability are achievable. However, the welfare effect of information is subtle: applicants may become worse off as they acquire more information.