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A model of random matching


  • Gilboa, Itzhak
  • Matsui, Akihiko


This paper presents a model of random matching between individuals chosen from large populations. We assume that the populations and the set of encounters are infinite but countable and that the encounters are i.i.d. random variables. Furthermore, the probability distribution on individuals according to which they are chosen for each encounter is "uniform", which also implies that it is only finitely additive. Although the probability measure which governs the whole matching process also fails to be (fully) sigma-additive, it still retains enough continuity properties to allow for the use of the law of large numbers. This, in turn, guarantees that the aggregate process will (almost surely) behave "nicely", i.e., that there will be no aggregate uncertainty.
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Suggested Citation

  • Gilboa, Itzhak & Matsui, Akihiko, 1992. "A model of random matching," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 185-197.
  • Handle: RePEc:eee:mateco:v:21:y:1992:i:2:p:185-197

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    References listed on IDEAS

    1. 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.
    2. Weiss, Ernst-August Jr., 1981. "Finitely additive exchange economies," Journal of Mathematical Economics, Elsevier, vol. 8(3), pages 221-240, October.
    3. Armstrong, Thomas E. & Richter, Marcel K., 1984. "The core-walras equivalence," Journal of Economic Theory, Elsevier, vol. 33(1), pages 116-151, June.
    4. Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-1169, September.
    5. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    6. 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.
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    Cited by:

    1. Alos-Ferrer, Carlos, 1999. "Dynamical Systems with a Continuum of Randomly Matched Agents," Journal of Economic Theory, Elsevier, vol. 86(2), pages 245-267, June.
    2. Richard T. Boylan, 1997. "Laws of Large Numbers for Dynamical Systems with Random Matched Individuals," Levine's Working Paper Archive 845, David K. Levine.
    3. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
    4. 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.
    5. repec:eee:jetheo:v:174:y:2018:i:c:p:124-183 is not listed on IDEAS
    6. Al-Najjar, Nabil I., 2004. "Aggregation and the law of large numbers in large economies," Games and Economic Behavior, Elsevier, vol. 47(1), pages 1-35, April.
    7. Daniela Puzzello & Konrad Podczeck, 2010. "Independent random matching with many types," 2010 Meeting Papers 652, Society for Economic Dynamics.
    8. Bester, Helmut, 2013. "Investments and the holdup problem in a matching market," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 302-311.
    9. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
    10. Edward J. Green & Ruilin Zhou, 2002. "Dynamic Monetary Equilibrium in a Random Matching Economy," Econometrica, Econometric Society, vol. 70(3), pages 929-969, May.
    11. Konrad Podczeck & Daniela Puzzello, 2012. "Independent random matching," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 1-29, May.
    12. Joosten, Reinoud, 1995. "Evolution, dynamics, and fixed points," Research Memorandum 005, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
    13. Golman, Russell, 2012. "Homogeneity bias in models of discrete choice with bounded rationality," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 1-11.
    14. Molzon, Robert & Puzzello, Daniela, 2010. "On the observational equivalence of random matching," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1283-1301, May.
    15. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    16. Itzhak Gilboa & Dov Samet, 1991. "Absorbent Stable Sets," Discussion Papers 935, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    17. Aliprantis, C.D. & Camera, G. & Puzzello, D., 2007. "A random matching theory," Games and Economic Behavior, Elsevier, vol. 59(1), pages 1-16, April.
    18. Russell Golman, 2011. "Why learning doesn’t add up: equilibrium selection with a composition of learning rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 719-733, November.
    19. Cho, In-Koo & Matsui, Akihiko, 2013. "Search theory, competitive equilibrium, and the Nash bargaining solution," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1659-1688.
    20. Molzon, Robert & Puzzello, Daniela, 2008. "Random Matching and Aggregate Uncertainty," MPRA Paper 8603, University Library of Munich, Germany.
    21. Edward J. Green & Ruilin Zhou, 1999. "Monetary Equilibrium from an Initial State: The Case Without Discounting," Macroeconomics 9902010, EconWPA.
    22. Karavaev, Andrei, 2008. "A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings," MPRA Paper 7445, University Library of Munich, Germany.
    23. Charalambos Aliprantis & Gabriele Camera & Daniela Puzzello, 2006. "Matching and anonymity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 415-432, October.
    24. Edward J. Green & Ruilin Zhou, 2001. "Price level uniformity in a random matching model with perfectly patient traders," Working Paper Series WP-01-17, Federal Reserve Bank of Chicago.

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