Information-Credible Stability in Matching with Incomplete Information

TL;DR

This paper introduces Information-Credible Pairwise Stability (ICPS), a new solution concept for matching markets with incomplete information that accounts for credible, costly information tests, refining existing stability notions and ensuring welfare improvements.

Contribution

It develops ICPS, a novel stability refinement incorporating credible testing, connecting belief-based and information-based stability, and demonstrating its existence, uniqueness, and welfare properties.

Findings

ICPS strictly refines Bayesian stability.

ICPS promotes positive assortative matching.

ICPS always exists and is unique under strong test power.

Abstract

In this paper, I develop a refinement of stability for matching markets with incomplete information. I introduce Information-Credible Pairwise Stability (ICPS), a solution concept in which deviating pairs can use credible, costly tests to reveal match-relevant information before deciding whether to block. By leveraging the option value of information, ICPS strictly refines Bayesian stability, rules out fear-driven matchings, and connects belief-based and information-based notions of stability. ICPS collapses to Bayesian stability when testing is uninformative or infeasible and coincides with complete-information stability when testing is perfect and free. I show that any ICPS-blocking deviation strictly increases total expected surplus, ensuring welfare improvement. I also prove that ICPS-stable allocations always exist, promote positive assortative matching, and are unique when the test power is sufficiently strong. The framework extends to settings with non-transferable utility, correlated types, and endogenous or sequential testing.