This work introduces a rigorous set-theoretic foundation of deterministic bilateral matching processes and studies systematically 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.
Aliprantis, C.D., G. Camera and D. Puzzello (2006). Matching and anonymity. Economic Theory 29, 415-432. doi: 10.1007/s00199-005-0024-z