Karavaev, Andrei (2008): A Theory of Continuum Economies with Independent Shocks and Matchings.

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Abstract
Numerous economic models employ a continuum of negligible agents with a sequence of idiosyncratic shocks and random matchings. Several attempts have been made to build a rigorous mathematical justification for such models, but these attempts have left many questions unanswered. In this paper, we develop a discrete time framework in which the major, desirable properties of idiosyncratic shocks and random matchings hold. The agents live on a probability space, and the probability distribution for each agent is naturally replaced by the population distribution. The novelty of this approach is in the assumption of unknown identity. Each agent believes that initially he was randomly and uniformly placed on the agent space, i.e., the agent's identity (the exact location on the agent space) is unknown to the agent.
Item Type:  MPRA Paper 

Original Title:  A Theory of Continuum Economies with Independent Shocks and Matchings 
Language:  English 
Keywords:  random matching, idiosyncratic shocks, the Law of Large Numbers, aggregate uncertainty, mixing 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C78  Bargaining Theory; Matching Theory D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D83  Search; Learning; Information and Knowledge; Communication; Belief E  Macroeconomics and Monetary Economics > E0  General > E00  General 
Item ID:  17113 
Depositing User:  Andrei Karavaev 
Date Deposited:  05. Sep 2009 07:59 
Last Modified:  15. Feb 2013 04:24 
References:  N.I. AlNajjar, Aggregation and the Law of Large Numbers in Large Economies, Games Econ. Behav. 47 (2004), 135. N.I. AlNajjar, Large Games and the Law of Large Numbers, Games Econ. Behav. 64 (2008), 134. C.D. Aliprantis, G. Camera, D. Puzzello, Matching and Anonymity, Econ. Theory 29 (2006), 415432. C.D. Aliprantis, G. Camera, D. Puzzello, A Random Matching Theory, Games Econ. Behav. 59 (2007), 116. C. AlosFerrer, Dynamical Systems with a Continuum of Randomly Matched Agents, J. Econ. Theory 86 (1999), 245267. C. AlosFerrer, Random Matching of Several Infinite Populations, Ann. Operations Res. 114 (2002), 3338. R.T. Boylan, Laws of Large Numbers for Dynamical Systems with Randomly Matched Individuals, J. Econ. Theory 57 (1992), 473504. R.T. Boylan, Continuous Approximation of Dynamical Systems with Randomly Matched Individuals, J. Econ. Theory 66 (1995), 615625. D. Duffie, Y. Sun, Existence of Independent Random Matching, Ann. Appl. Probab. 17 (2007), 386419. M. Feldman, C. Gilles, An Expository Note on Individual Risk without Aggregate Uncertainty, J. Econ. Theory 35 (1985), 2632. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, Wiley & Sons, New York, 1971. D. Gale, Bargaining and Competition Part I: Characterization, Econometrica 54 (1986), 785806. I. Gilboa, A. Matsui, A Model of Random Matching, J. Math. Econ. 21 (1992), 185197. E.J. Green, IndividualLevel Randomness in a Nonatomic Population, Working paper, University of Minnesota, 1994. E.J. Green, R. Zhou, Dynamic Monetary Equilibrium in a Random Matching Economy, Econometrica 70 (2002), 929969. P. Halmos, Naive Set Theory, SpringerVerlag, New York, 1974. P.J. Hammond, Y. Sun, Monte Carlo Simulation of Macroeconomic Risk with a Continuum of Agents: The Symmetric Case, Econ. Theory 21 (2003), 743766. P.J. Hammond, Y. Sun, Monte Carlo Simulation of Macroeconomic Risk with a Continuum of Agents: The General Case, Econ. Theory 36 (2008), 303325. K.L. Judd, The Law of Large Numbers with a Continuum of IID Random Variables, J. Econ. Theory 35 (1985), 1925. A.N. Kolmogorov, Foundations of the Theory of Probability, Chelsea Publishing Company, New York, 1956. A. McLennan, H. Sonnenschein, Sequential Bargaining as a Noncooperative Foundation for Walrasian Equilibrium, Econometrica 59 (1991), 13951424. Y. Sun, A Theory of Hypernite Processes: The Complete Removal of Individual Uncertainty via Exact LLN, J. Math. Econ. 29 (1998), 419503. H. Uhlig, A Law of Large Numbers for Large Economies, Econ. Theory 8 (1996), 4150. A.D. Wentzell, A Course in the Theory of Stochastic Processes, McGrawHill, New York, 1981. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/17113 