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The Exact Law of Large Numbers for Independent Random Matching

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Listed author(s):
  • 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.

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File URL: http://www.stanford.edu/~duffie/lln-I.pdf
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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 122247000000000328.

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Date of creation: 01 Sep 2004
Handle: RePEc:cla:levrem:122247000000000328
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Find related papers by JEL classification:
  • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
  • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
  • E00 - Macroeconomics and Monetary Economics - - General - - - General

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Cited by:

  1. Alain B\'elanger & Gaston Giroux, 2012. "Information Percolation: Some General Cases with an Application to Econophysics," Papers 1202.5251, arXiv.org.
  2. Hedlund, Jonas & Oyarzun, Carlos, 2016. "Imitation in Heterogeneous Populations," Working Papers 0625, University of Heidelberg, Department of Economics.
  3. Gregory Connor, 2009. "The Risky Lending Gap," Economics, Finance and Accounting Department Working Paper Series n2010809.pdf, Department of Economics, Finance and Accounting, National University of Ireland - Maynooth.
  4. Alger, Ingela & Weibull, Jörgen, 2014. "Evolution leads to Kantian morality," TSE Working Papers 14-504, Toulouse School of Economics (TSE), revised Jun 2015.
  5. Maurizio Iacopetta, 2016. "Commercial Revolutions, Search, and Development," 2016 Meeting Papers 1394, Society for Economic Dynamics.
  6. Marcel Nutz, 2016. "A Mean Field Game of Optimal Stopping," Papers 1605.09112, arXiv.org.
  7. Duffie, Darrell & Qiao, Lei & Sun, Yeneng, 2015. "Dynamic Directed Random Matching," Research Papers 3359, Stanford University, Graduate School of Business.
  8. Maurizio Iacopetta, 2014. "dynamics of assets liquidity and inequality in economies with decentralized markets," Working Papers hal-01099374, HAL.
  9. repec:eee:jeborg:v:137:y:2017:i:c:p:339-360 is not listed on IDEAS
  10. Maurizion Iacopetta, 2016. "Commercial revolutions, search, and development," Documents de Travail de l'OFCE 2016-08, Observatoire Francais des Conjonctures Economiques (OFCE).
  11. Takako Fujiwara-Greve & Masahiro Okuno-Fujiwara & Nobue Suzuki, 2015. "Efficiency may improve when defectors exist," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(3), pages 423-460, November.
  12. Takako Fujiwara-Greve & Masahiro Okuno-Fujiwara, 2013. "Diverse Behavior Patterns in a Symmetric Society with Voluntary Partnerships," Working Papers e62, Tokyo Center for Economic Research.
  13. Karavaev, Andrei, 2008. "A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings," MPRA Paper 7445, University Library of Munich, Germany.
  14. Schmitt, Rebecca, 2015. "Incorporating Phenotype Plasticity into the Indirect Evolutionary Approach," MPRA Paper 65734, University Library of Munich, Germany.

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