The exact law of large numbers for independent random matching

This paper provides micro-foundations 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. This work was initiated in July 2000 while the second author visited Stanford University. We are grateful for comments from Pierre-Olivier Weill and Zhixiang Zhang. Graduate School of Business, Stanford University, Stanford, CA 94305-5015. e-mail: [email protected] Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543; and Department of Economics, National University of Singapore, 1 Arts Link, Singapore 117570. e-mail: [email protected]