TY  - JOUR
AU  - Duffie,Darrell
AU  - Sun,Yeneng
TI  - The Exact Law of Large Numbers for Independent Random Matching
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 17280
PY  - 2011
Y2  - August 2011
UR  - http://www.nber.org/papers/w17280
L1  - http://www.nber.org/papers/w17280.pdf
N1  - Author contact info:
Darrell Duffie
Graduate School of Business
Stanford University
Stanford, CA  94305-5015
Tel: 650/723-1976
Fax: 650/725-7979
E-Mail: duffie@stanford.edu

Yeneng Sun
National University of Singapore
Department of Economics
1 Arts Link
Singapore 117570
Republic of Singapore
E-Mail: ynsun@nus.edu.sg
AB  - 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.
ER  -