Matching and anonymity

This work introduces a set-theoretic foundation of deterministic bilateral matching processes and studies their properties. In particular, it formalizes a link between matching and informational constraints by developing a notion of anonymity that is based on the agents’ matching histories. It also explains why and how various matching processes generate different degrees of “informational isolation” in the economy. We illustrate the usefulness of our approach to modeling matching frameworks by discussing the classical turnpike model of Townsend.This research is supported in part by the NSF grants EIA-0075506, SES-0128039, DMS-0437210, and ACI-0325846. We thank two anonymous referees for constructive comments that improved the exposition of the paper. We also thank the participants in seminars at the University of Aarhus, Purdue University, University of Texas at Austin, and at the XI Meeting on Real Analysis and Measure Theory in 2004, the spring 2004 Midwest Economic Theory Meeting, the summer 2004 North American and European Econometric Society meetings.