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- Dynamical Systems With A Continuum Of Randomly Matched Agents

Author

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  • Carlos Alós-Ferrer

    (Universidad de Alicante)

Abstract

Many models postulate a continuum of agents of finitely many different types who are repeatedly randomly matched in pairs to perform certain activities (e.g. play a game) which may in turn make their types change. The random matching process is usually left unspecified, and some Law of Large Numbers is informally invoked to justify a deterministic approximation of the resulting stochastic system. Nevertheless, it is well-know that such laws of large numbers may not hold in this framework. This work shows that there exist random matching processes over a continuum of agents satisfying properties which are sufficient to simplify the analysis of the stochastic system. Moreover, the evolution of the population frequencies of types induced by this system can be described (almost surely) through a set of deterministic equations.

Suggested Citation

  • 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).
    • Handle: RePEc:ivi:wpasad:1998-08
    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. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
    3. Gilboa, Itzhak & Matsui, Akihiko, 1992. "A model of random matching," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 185-197.
    4. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
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    7. Michael Peters, 1997. "On the Equivalence of Walrasian and Non-Walrasian Equilibria in Contract Markets: The Case of Complete Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(2), pages 241-264.
    8. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-1454, September.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    evolution; random matching; law of large numbers;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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