02122cam a22002657 4500001000700000003000500007005001700012008004100029100002100070245012100091260006600212490004200278500001700320520091000337530006101247538007201308538003601380690007001416690015901486700001701645710004201662830007701704856003801781856003701819w17280NBER20150905135941.0150905s2011 mau||||fs|||| 000 0 eng d1 aDuffie, Darrell.14aThe Exact Law of Large Numbers for Independent Random Matchingh[electronic resource] /cDarrell Duffie, Yeneng Sun. aCambridge, Mass.bNational Bureau of Economic Researchc2011.1 aNBER working paper seriesvno. w17280 aAugust 2011.3 aThis 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC02 - Mathematical Methods2Journal of Economic Literature class. 7aD83 - Search • Learning • Information and Knowledge • Communication • Belief • Unawareness2Journal of Economic Literature class.1 aSun, Yeneng.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w17280.4 uhttp://www.nber.org/papers/w1728041uhttp://dx.doi.org/10.3386/w17280