Abstract
Random matching models with a continuum population are widely used in economics to study environments where agents interact in small coalitions. This paper provides foundations to such models. In particular, the paper establishes an existence result for random matchings that are universal in the sense that certain desirable properties are satisfied for any assignment of types to agents. The result applies to infinitely many types of agents, thus covering random matching models which are currently used in the literature without a foundation. Furthermore, the paper provides conditions guaranteeing uniqueness of random matching.
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References
Aliprantis C.D., Camera G., Puzzello D.: Matching and anonymity. Econ Theory 29, 415–432 (2006)
Alós-Ferrer C.: Dynamical systems with a continuum of randomly matched agents. J Econ Theory 86, 245–267 (1999)
Alós-Ferrer C.: Random matching of several infinite populations. Ann Oper Res 114, 33–38 (2002)
Boylan R.: Laws of large numbers for dynamical systems with randomly matched individuals. J Econ Theory 57, 473–504 (1992)
Boylan R.: Continuous approximation of dynamical systems with randomly matched individuals. J Econ Theory 66, 615–625 (1992)
Cavalcanti R., Puzzello D.: Stationarity without degeneracy in a model of commodity money. Econ Theory 43, 263–280 (2010)
Duffie D., Sun Y.N.: Existence of independent random matching. Ann Appl Probab 17, 386–419 (2007)
Duffie, D., Sun, Y.N. The Exact Law of Large Numbers for Independent Random Matching. Mimeo (2010)
Fremlin D.H.: Measure Theory, vol. 2, Broad Foundations. Torres Fremlin, Colchester (2001)
Fremlin D.H.: Measure Theory, vol. 4, Topological Measure Spaces. Torres Fremlin, Colchester (2003)
Fremlin D.H.: Measure Theory, vol. 5, Set-Theoretic Measure Theory. Torres Fremlin, Colchester (2008)
Gilboa I., Matsui A.: A model of random matching. J Math Econ 21, 185–197 (1992)
Green E., Zhou R.: Dynamic monetary equilibrium in a random matching economy. Econometrica 70, 929–969 (2002)
Hildenbrand W.: Core and Equilibria of a Large Economy. Princeton University Press, Princeton (1974)
Hofbauer, J., Oechssler, J., Riedel, F.: Brown-von Neumann-Nash dynamics: the continuous strategy case. Tech. Rep. 05-41, Sonderforschungsbereich 504 Publications, Universität Mannheim & Sonderforschungsbereich 504 (2008)
Kandori M.: Social norms and community enforcement. Rev Econ Stud 59, 63–80 (1992)
Kandori M., Mailath G., Rob R.: Learning, mutation and long run equilibria in games. Econometrica 61, 29–56 (1993)
Kiyotaki N., Wright R.: On money as a medium of exchange. J Polit Economy 97, 927–954 (1989)
Lagos R., Wright R.: A unified framework for monetary theory and policy analysis. J Polit Economy 113, 463–484 (2005)
Molico M.: The distribution of money and prices in search equilibrium. Int Econ Rev 47, 701–722 (2006)
Molzon, R. Puzzello, D. Random Matching and Aggregate Uncertainty. Mimeo (2009)
Molzon R., Puzzello D.: On the observational equivalence of random matching. J Econ Theory 145, 1283–1301 (2010)
Mortensen D., Pissarides C.: Job creation and job destruction in the theory of unemployment. Rev Econ Stud 61, 397–415 (1994)
Oechssler J., Riedel F.: On the dynamic foundations of evolutionary stability in continuous models. J Econ Theory 107, 223–252 (2002)
Okuno-Fujiwara M., Postlewaite A.: Social norms and random matching games. Games Econ Behav 9, 79–109 (1995)
Podczeck K.: On existence of rich Fubini extensions. Econ Theory 45, 1–22 (2010)
Sandholm W.: Potential games with continuous player sets. J Econ Theory 97, 81–108 (2001)
Shi S.: A divisible search model of fiat money. Econometrica 65, 75–102 (1997)
Sun Y.N.: The exact law of large numbers via Fubini extension and characterization of insurable risks. J Econ Theory 126, 31–69 (2006)
Sun Y.N., Yannelis N.C.: Ex ante efficiency implies incentive compatibility. Econ Theory 36, 35–55 (2008)
Takahashi S.: Community enforcement when players observe partners’ past play. J Econ Theory 145, 42–62 (2010)
van Veelen M., Spreij P.: Evolution in games with a continuous action space. Econ Theory 39, 355–376 (2009)
Zhu T.: Existence of a monetary steady state in a matching model: divisible money. J Econ Theory 123, 135–160 (2005)
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We thank an anonymous referee for valuable comments and for suggestions on how to improve the presentation of the material of this paper.
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Podczeck, K., Puzzello, D. Independent random matching. Econ Theory 50, 1–29 (2012). https://doi.org/10.1007/s00199-010-0584-4
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DOI: https://doi.org/10.1007/s00199-010-0584-4