The Exact Law of Large Numbers for Independent Random Matching

43 Pages Posted: 12 Aug 2011 Last revised: 20 Mar 2023

See all articles by Darrell Duffie

Darrell Duffie

Stanford University - Graduate School of Business; National Bureau of Economic Research (NBER); Canadian Derivatives Institute

Yeneng Sun

National University of Singapore (NUS)

Date Written: August 2011

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.

Suggested Citation

Duffie, James Darrell and Sun, Yeneng, The Exact Law of Large Numbers for Independent Random Matching (August 2011). NBER Working Paper No. w17280, Available at SSRN: https://ssrn.com/abstract=1908568

James Darrell Duffie (Contact Author)

Stanford University - Graduate School of Business ( email )

655 Knight Way
Knight Management Center
Stanford, CA 94305-7298
United States
650-723-1976 (Phone)
650-725-8916 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Canadian Derivatives Institute ( email )

3000, chemin de la Côte-Sainte-Catherine
Montréal, Québec H3T 2A7
Canada

Yeneng Sun

National University of Singapore (NUS) ( email )

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
41
Abstract Views
709
PlumX Metrics