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.