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A Model of Random Matching

Author

Listed:
  • Itzhak Gilboa

    (Northwestern University [Evanston])

  • Akihiko Matsui

    (University of Pennsylvania)

Abstract

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.

Suggested Citation

  • Itzhak Gilboa & Akihiko Matsui, 1992. "A Model of Random Matching," Post-Print hal-00753230, HAL.
    • Handle: RePEc:hal:journl:hal-00753230
    DOI: 10.1016/0304-4068(92)90010-5
    as

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    References listed on IDEAS

    as
    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, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    5. Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-1169, September.
    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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    Keywords

    Random Matching;

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