Podczeck, Konrad and Puzzello, Daniela
(2009):
*Independent Random Matching.*
Forthcoming in: Economic Theory

Preview |
PDF
MPRA_paper_27687.pdf Download (208kB) | Preview |

## 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.

Item Type: | MPRA Paper |
---|---|

Original Title: | Independent Random Matching |

Language: | English |

Keywords: | Random matching; Involution; Independence; Continuum population; Fubini extension |

Subjects: | C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory C - Mathematical and Quantitative Methods > C0 - General > C00 - General C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games |

Item ID: | 27687 |

Depositing User: | Daniela Puzzello |

Date Deposited: | 27 Dec 2010 11:03 |

Last Modified: | 28 Sep 2019 06:46 |

References: | Aliprantis, C. D., G. Camera, and D. Puzzello (2006): “Matching and anonymity,” Economic Theory, 29, 415–432. Alós-Ferrer, C. (1999): “Dynamical systems with a continuum of randomly matched agents,” Journal of Economic Theory, 86, 245–267. Alós-Ferrer,(2002): “Random matching of several infinite populations,” Annals of Operations Research, 114, 33–38. Boylan, R. (1992): “Laws of large numbers for dynamical systems with randomly matched individuals,” Journal of Economic Theory, 57, 473–504. Boylan, R. (1995): “Continuous approximation of dynamical systems with randomly matched individuals,” Journal of Economic Theory, 66, 615–625. Cavalcanti, R. and D. Puzzello (2010): “Stationarity without degeneracy in a model of commodity money,” Economic Theory, 43, 263–280. Duffie, D. and Y. Sun (2007): “Existence of independent random matching,” The Annals of Applied Probability, 17, 386–419. Duffie, D. and Y. Sun(2010): “The exact law of large numbers for independent random matching,” mimeo. Fremlin, D. H. (2001): Measure Theory, vol. 2: Broad Foundations, Colchester: Torres Fremlin. Fremlin, D. H.(2003): Measure Theory, vol. 4: Topological Measure Spaces, Colchester: Torres Fremlin. Fremlin, D. H.(2008): Measure Theory, vol. 5: Set-Theoretic Measure Theory, Colchester: Torres Fremlin. Gilboa, I. and A. Matsui (1992): “A model of random matching,” Journal of Mathematical Economics, 21, 185–197. Green, E. and R. Zhou (2002): “Dynamic monetary equilibrium in a random matching economy,” Econometrica, 70, 929–969. Hildenbrand, W. (1974): Core and Equilibria of a Large Economy, Princeton, New Jersey: Princeton University Press. Hofbauer, J., J. Oechssler, and F. Riedel (2008): “Brown-von Neumann-Nash dynamics: the continuous strategy case,” Tech. Rep. 05-41, Sonderforschungsbereich 504 Publications, Universität Mannheim & Sonderforschungsbereich 504. Kandori, M. (1992): “Social norms and community enforcement,” Review of Economic Studies, 59, 63–80. Kandori, M., G. Mailath, and R. Rob (1993): “Learning, mutation and long run equilibria in games,” Econometrica, 61, 29–56. Kiyotaki, N. and R. Wright (1989): “On money as a medium of exchange,” Journal of Political Economy, 97, 927–954. Lagos, R. and R. Wright (2005): “A unified framework for monetary theory and policy analysis,” Journal of Political Economy, 113, 463–484. Molico, M. (2006): “The distribution of money and prices in search equilibrium,” International Economic Review, 47, 701–722. Molzon, R. and D. Puzzello (2009): “Random matching and aggregate uncertainty,” Mimeo. Molzon, R. and D. Puzzello(2010): “On the observational equivalence of random matching,” Journal of Economic Theory, 145, 1283-1301. Mortensen, D. and C. Pissarides (1994): “Job creation and job destruction in the theory of unemployment,” Review of Economic Studies, 61, 397–415. Oechssler, J. and F. Riedel (2002): “On the dynamic foundations of evolutionary stability in continuous models,” Journal of Economic Theory, 107, 223– 252. Okuno-Fujiwara, M. and A. Postlewaite (1995): “Social norms and random matching games,” Games and Economic Behavior, 9, 79–109. Podczeck, K. (2010): “On existence of rich Fubini extensions,” Economic Theory, in press. Sandholm, W. (2001): “Potential games with continuous player sets,” Journal of Economic Theory, 97, 81–108. Shi, S. (1997): “A divisible search model of fiat money,” Econometrica, 65, 75–102. Sun, Y. N. (2006): “The exact law of large numbers via Fubini extension and characterization of insurable risks,” Journal of Economic Theory, 126, 31–69. Sun, Y. N. and N. C. Yannelis (2008): “Ex ante efficiency implies incentive compatibility,” Economic Theory, 36, 35–55. Takahashi, S. (2010): “Community enforcement when players observe partners’ past play,” Journal of Economic Theory, 145, 42–62. van Veelen, M. and P. Spreij (2009): “Evolution in games with a continuous action space,” Economic Theory, 39, 355–376. Zhu, T. (2005): “Existence of a monetary steady state in a matching model: divisible money,” Journal of Economic Theory, 123, 135–160. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/27687 |