The (Non)-Existence of Stable Mechanisms in Incomplete Information Environments

TL;DR

This paper investigates the stability of matching mechanisms under incomplete information, revealing that uncertainty about preferences leads to vulnerabilities where agents can profitably deviate, unlike in complete information settings.

Contribution

It demonstrates that no stable mechanism exists in incomplete information environments, highlighting the fragility of stability when agents lack full preference knowledge.

Findings

Mechanisms are susceptible to group deviations under preference uncertainty.

Single pair deviations occur when agents are uncertain about their own preferences.

Stability results from complete information do not extend to incomplete information settings.

Abstract

We consider two-sided matching markets, and study the incentives of agents to circumvent a centralized clearing house by signing binding contracts with one another. It is well-known that if the clearing house implements a stable match and preferences are known, then no group of agents can profitably deviate in this manner. We ask whether this property holds even when agents have incomplete information about their own preferences or the preferences of others. We find that it does not. In particular, when agents are uncertain about the preferences of others, every mechanism is susceptible to deviations by groups of agents. When, in addition, agents are uncertain about their own preferences, every mechanism is susceptible to deviations in which a single pair of agents agrees in advance to match to each other.