IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

The exact law of large numbers for independent random matching

  • Duffie, Darrell
  • Sun, Yeneng

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/pii/S002205311200004X
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 3 ()
Pages: 1105-1139

as
in new window

Handle: RePEc:eee:jetheo:v:147:y:2012:i:3:p:1105-1139
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Trejos, Alberto & Wright, Randall, 1995. "Search, Bargaining, Money, and Prices," Journal of Political Economy, University of Chicago Press, vol. 103(1), pages 118-41, February.
  2. Kiyotaki, Nobuhiro & Wright, Randall, 1993. "A Search-Theoretic Approach to Monetary Economics," American Economic Review, American Economic Association, vol. 83(1), pages 63-77, March.
  3. Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Wiley Blackwell, vol. 66(2), pages 363-93, April.
  4. Edward J. Green, 1994. "Individual Level Randomness in a Nonatomic Population," GE, Growth, Math methods 9402001, EconWPA.
  5. Dimitri Vayanos & Tan Wang, 2004. "Search and endogenous concentration of liquidity in asset markets," LSE Research Online Documents on Economics 455, London School of Economics and Political Science, LSE Library.
  6. Edward J. Green & Ruilin Zhou, 2000. "Dynamic monetary equilibrium in a random-matching economy," Working Paper Series WP-00-1, Federal Reserve Bank of Chicago.
  7. Binmore, K. & Samuelson, L., 1995. "Evolutionary Drift and Equilibrium Selection," Working papers 9529, Wisconsin Madison - Social Systems.
  8. Fudenberg, Drew & Levine, David K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-73, May.
  9. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
  10. Frankel, David M. & Burdzy, Krzysztof & Pauzner, Ady, 2001. "Fast Equilibrium Selection by Rational Players Living in a Changing World," Staff General Research Papers 11923, Iowa State University, Department of Economics.
  11. Hosios, Arthur J, 1990. "On the Efficiency of Matching and Related Models of Search and Unemployment," Review of Economic Studies, Wiley Blackwell, vol. 57(2), pages 279-98, April.
  12. McLennan, Andrew & Sonnenschein, Hugo, 1991. "Sequential Bargaining as a Noncooperative Foundation for Walrasian Equilibrium," Econometrica, Econometric Society, vol. 59(5), pages 1395-1424, September.
  13. Itzhak Gilboa & Akihiko Matsui, 1990. "A Model of Random Matching," Discussion Papers 887, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Diamond, Peter A, 1982. "Aggregate Demand Management in Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 90(5), pages 881-94, October.
  15. Anderson, Robert M., 1991. "Non-standard analysis with applications to economics," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 39, pages 2145-2208 Elsevier.
  16. Wolinsky, Asher, 1987. "Information Revelation in a Market with Pairwise Meetings," The Warwick Economics Research Paper Series (TWERPS) 284, University of Warwick, Department of Economics.
  17. Harrington, Joseph E, Jr, 1998. "The Social Selection of Flexible and Rigid Agents," American Economic Review, American Economic Association, vol. 88(1), pages 63-82, March.
  18. Mortensen, Dale T & Pissarides, Christopher A, 1994. "Job Creation and Job Destruction in the Theory of Unemployment," Review of Economic Studies, Wiley Blackwell, vol. 61(3), pages 397-415, July.
  19. Darrell Duffie & Nicolae Garleanu & Lasse Heje Pedersen, 2006. "Valuation in Over-the-Counter Markets," NBER Working Papers 12020, National Bureau of Economic Research, Inc.
  20. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
  21. Diamond, Peter A., 1971. "A model of price adjustment," Journal of Economic Theory, Elsevier, vol. 3(2), pages 156-168, June.
  22. Darrell Duffie & Nicolae Garleanu & Lasse Heje Pedersen, 2005. "Over-the-Counter Markets," Econometrica, Econometric Society, vol. 73(6), pages 1815-1847, November.
  23. Peter Rupert & Martin Schindler & Andrei Shevchenko & Randall Wright, 2000. "The search-theoretic approach to monetary economics: a primer," Economic Review, Federal Reserve Bank of Cleveland, issue Q IV, pages 10-28.
  24. Dekel, E. & Scotchmer, S., 1999. "On the Evolution of Attitudes Towards Risk in Winner-Take-All Games," Papers 4-99, Tel Aviv.
  25. Diamond, Peter & Yellin, Joel, 1990. "Inventories and Money Holdings in a Search Economy," Econometrica, Econometric Society, vol. 58(4), pages 929-50, July.
  26. Molzon, Robert & Puzzello, Daniela, 2010. "On the observational equivalence of random matching," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1283-1301, May.
  27. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
  28. John Krainer & Stephen F. LeRoy, 2002. "Equilibrium valuation of illiquid assets," Economic Theory, Springer, vol. 19(2), pages 223-242.
  29. Carlos Alós-Ferrer, 1998. "- Dynamical Systems With A Continuum Of Randomly Matched Agents," Working Papers. Serie AD 1998-08, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  30. Aliprantis, C. D. & Camera, G. & Puzzelo, D., 2004. "A Random Matching Theory," Purdue University Economics Working Papers 1168, Purdue University, Department of Economics.
  31. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
  32. Weill, Pierre-Olivier, 2008. "Liquidity premia in dynamic bargaining markets," Journal of Economic Theory, Elsevier, vol. 140(1), pages 66-96, May.
  33. Sun, Yeneng & Zhang, Yongchao, 2008. "Individual Risk and Lebesgue Extension without Aggregate Uncertainty," MPRA Paper 7448, University Library of Munich, Germany.
  34. Gale, Douglas M, 1986. "Bargaining and Competition Part II: Existence," Econometrica, Econometric Society, vol. 54(4), pages 807-18, July.
  35. Boylan, Richard T., 1992. "Laws of large numbers for dynamical systems with randomly matched individuals," Journal of Economic Theory, Elsevier, vol. 57(2), pages 473-504, August.
  36. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-54, August.
  37. Mortensen, Dale T, 1982. "Property Rights and Efficiency in Mating, Racing, and Related Games," American Economic Review, American Economic Association, vol. 72(5), pages 968-79, December.
  38. Merz, Monika, 1999. "Heterogeneous job-matches and the cyclical behavior of labor turnover," Journal of Monetary Economics, Elsevier, vol. 43(1), pages 91-124, February.
  39. Sun, Yeneng, 1998. "A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN1," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 419-503, May.
  40. Cole, Harold L & Rogerson, Richard, 1999. "Can the Mortensen-Pissarides Matching Model Match the Business-Cycle Facts?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 933-59, November.
  41. Charalambos Aliprantis & Gabriele Camera & Daniela Puzzello, 2006. "Matching and anonymity," Economic Theory, Springer, vol. 29(2), pages 415-432, October.
  42. Gale, Douglas M, 1986. "Bargaining and Competition Part I: Characterization," Econometrica, Econometric Society, vol. 54(4), pages 785-806, July.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:147:y:2012:i:3:p:1105-1139. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.