Working Paper: NBER ID: w17280
Authors: Darrell Duffie; Yeneng Sun
Abstract: This paper provides a mathematical foundation for independent random matching of a large population, as widely used in the economics literature. We consider both static and dynamic systems with random mutation, partial matching arising from search, and type changes induced by matching. Under independence assumptions at each randomization step, we show that there is an almost-sure constant cross-sectional distribution of types in a large population, and moreover that the multi-period cross-sectional distribution of types is deterministic and evolves according to the transition matrices of the type process of a given agent. We also show the existence of a joint agent-probability space, and randomized mutation, partial matching and match-induced type-changing functions that satisfy appropriate independence conditions, where the agent space is an extension of the classical Lebesgue unit interval.
Keywords: Law of large numbers; Independent random matching; Economics; Mathematics
JEL Codes: C02; D83
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| independent random matching models for continuum populations (C78) | almost-sure constant cross-sectional distribution of types (C46) |
| independence of agent types (L85) | time evolution of the cross-sectional distribution of types (D39) |
| Markov conditional independence (D80) | deterministic evolution of type distributions (C46) |
| random mutation and matching-induced type changes (C78) | impact on the distribution of types (D39) |
| independence assumptions during randomization steps (C90) | independence of agent types (L85) |
| agent-level Markov chain (C69) | time evolution of the cross-sectional distribution of types (D39) |