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- Dynamical Systems With A Continuum Of Randomly Matched Agents

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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
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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.
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    6. Michael Peters, 1995. "On the Equivalence of Walrasian and Non-Walrasian Equilibria in Contract Markets: The case of Complete Contracts," Working Papers peters-95-01, University of Toronto, Department of Economics.
    7. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-1454, September.
    8. McLennan, Andrew & Sonnenschein, Hugo, 1991. "Sequential Bargaining as a Noncooperative Foundation for Walrasian Equilibrium," Econometrica, Econometric Society, vol. 59(5), pages 1395-1424, September.
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    Cited by:

    1. 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.
    2. Mendolicchio, Concetta & Paolini, Dimitri & Pietra, Tito, 2012. "Investments in education and welfare in a two-sector, random matching economy," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 367-385.
    3. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
    4. Andreas Ramsauer, 1999. "Heterogeneous Discount Factors in an Assignment Model with Search Frictions," Vienna Economics Papers 9807, University of Vienna, Department of Economics.
    5. 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.
    6. Carlos Alós-Ferrer & Klaus Ritzberger, 2013. "Large extensive form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 75-102, January.
    7. 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.
    8. Molzon, Robert & Puzzello, Daniela, 2010. "On the observational equivalence of random matching," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1283-1301, May.
    9. Squintani, Francesco, 2003. "Moral hazard, renegotiation, and forgetfulness," Games and Economic Behavior, Elsevier, vol. 44(1), pages 98-113, July.
    10. Garcia-Martinez, Jose A., 2010. "Selectivity in hierarchical social systems," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2471-2482, November.
    11. Garcia-Martinez, Jose A., 2012. "An Unexpected Role of Local Selectivity in Social Promotion," MPRA Paper 36324, University Library of Munich, Germany.
    12. Francesco Squintani, 1999. "Games with Small Forgetfulness," Discussion Papers 1273, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Lee, Manjong, 2013. "Coexistence and welfare cost of inflation," Journal of Macroeconomics, Elsevier, vol. 36(C), pages 23-32.
    14. 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.
    15. De Fraja, Gianni & Sákovics, József, 2012. "Exclusive nightclubs and lonely hearts columns: Non-monotone participation in optional intermediation," Journal of Economic Behavior & Organization, Elsevier, vol. 84(2), pages 618-632.
    16. Molzon, Robert & Puzzello, Daniela, 2008. "Random Matching and Aggregate Uncertainty," MPRA Paper 8603, University Library of Munich, Germany.
    17. Mihaela Schaar & Jie Xu & William Zame, 2013. "Efficient online exchange via fiat money," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 211-248, October.
    18. Hsiaw, Alice, 2014. "Learning tastes through social interaction," Journal of Economic Behavior & Organization, Elsevier, vol. 107(PA), pages 64-85.
    19. Vega-Redondo, Fernando, 2000. "Unfolding Social Hierarchies," Journal of Economic Theory, Elsevier, vol. 90(2), pages 177-203, February.
    20. Francesco Squintani, 1999. "Moral Hazard," Discussion Papers 1269, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    21. Karavaev, Andrei, 2008. "A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings," MPRA Paper 7445, University Library of Munich, Germany.
    22. Carlos Alós-Ferrer, 2000. "Finite Population Dynamics and Mixed Equilibria," Vienna Economics Papers 0008, University of Vienna, Department of Economics.
    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.

    More about this item

    Keywords

    evolution; random matching; law of large numbers;

    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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