Stable Matching with Incomplete Information

Abstract

We formulate a notion of stable outcomes in matching problems with one‐sided asymmetric information. The key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make. We show that the set of stable outcomes is nonempty in incomplete‐information environments, and is a superset of the set of complete‐information stable outcomes. We then provide sufficient conditions for incomplete‐information stable matchings to be efficient. Lastly, we define a notion of price‐sustainable allocations and show that the set of incomplete‐information stable matchings is a subset of the set of such allocations.

Stability with one-sided incomplete information

“…If a matching endures, it becomes common knowledge among agents that the types of workers are such that there are no blocking opportunities; such matching outcomes are stable. Liu et al (2014) point out that this is similar in spirit to Holmstrom and Myerson (1983)'s notion of durable mechanisms.…”

“…If the set {(μ, w)} is ex ante self-stabilizing then, by definition, μ is a complete-information stable matching at w. Additional results are gathered in Lemmas 1 and 2 below; similar results are obtained in Liu et al (2014) for a model with side payments.…”

“…There are several papers on matching with incomplete information and interdependent preferences, in addition to Liu et al (2014). Pomatto (2015) investigates the epistemic foundations of Liu at al.…”

“…In this section, I present a definition of blocking and stability that adapts, to a model without side payments, the definition of Liu et al (2014).…”

“…Ex ante stability adapts to a NTU model, a definition of stability under one-sided incomplete information introduced by Liu et al (2014) in a matching model with transferrable utility (TU) and side payments. A firm j participates in a block with a worker i only if j is better off with all admissible types of i, i.e., with all types of worker i that are better off in the contemplated block.…”