Incomplete Information and Matching of Likes: A Mechanism Design Approach

TL;DR

This paper investigates the design of mechanisms for stable matchings in markets with incomplete information, showing conditions under which certain mechanisms are incentive compatible and highlighting limitations when both sides have incomplete information.

Contribution

It introduces a mechanism design framework for stable matchings with incomplete information, identifying when assortative matching mechanisms are incentive compatible and their limitations.

Findings

Assortative matching with full type disclosure is incentive compatible.

Limiting information to firms' lower contour sets remains incentive compatible.

Assortative matching is not implementable when both sides have incomplete information.

Abstract

We study the implementability of stable matchings in a two-sided market model with one-sided incomplete information. Firms' types are publicly known, whereas workers' types are private information. A mechanism generates a matching and additional announcements to the firms at each report profile of workers' types. When agents' preferences are increasing in the types of their matched partner, we show that the assortative matching mechanism which publicly announces the entire set of reported types is incentive compatible. Furthermore, any mechanism that limits information disclosure to firms' lower contour sets of reported types remains incentive compatible. However, when information is incomplete on both sides of the market, assortative matching is no longer implementable.