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- Dynamical Systems With A Continuum Of Randomly Matched Agents

  • Carlos Alós-Ferrer

    (Universidad de Alicante)

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.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1998-08.pdf
File Function: Fisrt version / Primera version, 1998
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Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 1998-08.

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Length: 31 pages
Date of creation: Apr 1998
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:1998-08
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  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. McLennan, Andrew & Sonnenschein, Hugo, 1991. "Sequential Bargaining as a Noncooperative Foundation for Walrasian Equilibrium," Econometrica, Econometric Society, vol. 59(5), pages 1395-1424, September.
  3. Gilboa, Itzhak & Matsui, Akihiko, 1992. "A model of random matching," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 185-197.
  4. Michael Peters, 1995. "On the Equivalence of Walrasian and Non-Walrasian Equilibria in Contract Markets: The case of Complete Contracts," GE, Growth, Math methods 9507001, EconWPA.
  5. Akihiko Matsui & Kiminori Matsuyama, 1990. "An Approach to Equilibrium Selection," Discussion Papers 970, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-54, September.
  7. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, June.
  8. 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.
  9. Boylan Richard T., 1995. "Continuous Approximation of Dynamical Systems with Randomly Matched Individuals," Journal of Economic Theory, Elsevier, vol. 66(2), pages 615-625, August.
  10. 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.
  11. 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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