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The exact law of large numbers for independent random matching

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  • Duffie, Darrell
  • Sun, Yeneng

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, Darrell & Sun, Yeneng, 2012. "The exact law of large numbers for independent random matching," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1105-1139.
  • Handle: RePEc:eee:jetheo:v:147:y:2012:i:3:p:1105-1139
    DOI: 10.1016/j.jet.2012.01.003
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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. Maurizion Iacopetta, 2016. "Commercial revolutions, search, and development," Documents de Travail de l'OFCE 2016-08, Observatoire Francais des Conjonctures Economiques (OFCE).
    4. 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.
    5. Duffie, Darrell & Qiao, Lei & Sun, Yeneng, 2018. "Dynamic directed random matching," Journal of Economic Theory, Elsevier, vol. 174(C), pages 124-183.
    6. Maurizio Iacopetta, 2016. "Commercial revolutions, search and development," Sciences Po publications 2016-08, Sciences Po.
    7. Maurizio Iacopetta, 2014. "Dynamics of assets liquidity and inequality in economies with decentralized markets," Sciences Po publications info:hdl:2441/2029nqlehl8, Sciences Po.
    8. 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.
    9. Alger, Ingela & Weibull, Jörgen W., 2014. "Evolution leads to Kantian morality," TSE Working Papers 14-504, Toulouse School of Economics (TSE), revised Jun 2015.
    10. Karavaev, Andrei, 2008. "A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings," MPRA Paper 7445, University Library of Munich, Germany.
    11. 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.
    12. Schmitt, Rebecca, 2015. "Incorporating Phenotype Plasticity into the Indirect Evolutionary Approach," MPRA Paper 65734, University Library of Munich, Germany.
    13. Alain B'elanger & Ndoun'e Ndoun'e & Roland Pongou, 2018. "Dark Markets with Multiple Assets: Segmentation, Asymptotic Stability, and Equilibrium Prices," Papers 1806.01924, arXiv.org.
    14. Marcel Nutz, 2016. "A Mean Field Game of Optimal Stopping," Papers 1605.09112, arXiv.org, revised Nov 2017.
    15. repec:spr:series:v:9:y:2018:i:3:d:10.1007_s13209-018-0180-6 is not listed on IDEAS
    16. repec:eee:jeborg:v:137:y:2017:i:c:p:339-360 is not listed on IDEAS
    17. repec:spr:joecth:v:65:y:2018:i:4:d:10.1007_s00199-017-1044-1 is not listed on IDEAS

    More about this item

    Keywords

    Independent random matching; Search; Exact law of large numbers; Population dynamics; Random mutation;

    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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