Consistent Conjectures in Dynamic Matching Markets

TL;DR

This paper introduces a framework for analyzing stability in two-sided dynamic matching markets using agents' conjectures about future matchings, establishing conditions for the existence of solutions and proposing new stability concepts.

Contribution

It develops a novel framework centered on agents' conjectures, identifies a key consistency condition for solutions, and introduces two new stability concepts for dynamic markets.

Findings

A sufficient condition called consistency ensures nonempty solutions.

Introduces continuation-value-respecting dynamic stability.

Extends Hafalir's solution concept to dynamic markets.

Abstract

We provide a framework to study stability notions for two-sided dynamic matching markets in which matching is one-to-one and irreversible. The framework gives center stage to the set of matchings an agent anticipates would ensue should they remain unmatched, which we refer to as the agent's conjectures. A collection of conjectures, together with a pairwise stability and individual rationality requirement given the conjectures, defines a solution concept for the economy. We identify a sufficient condition--consistency--for a family of conjectures to lead to a nonempty solution (cf. Hafalir, 2008). As an application, we introduce two families of consistent conjectures and their corresponding solution concepts: continuation-value-respecting dynamic stability, and the extension to dynamic markets of the solution concept in Hafalir (2008), sophisticated dynamic stability.