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

PDF
MPRA_paper_7445.pdf Download (286Kb)  Preview 
Abstract
Many economic models use a continuum of negligible agents to avoid considering one person's effect on aggregate characteristics of the economy. Along with a continuum of agents, these models often incorporate a sequence of independent shocks and random matchings. Despite frequent use of such models, there are still unsolved questions about their mathematical justification. In this paper we construct a discrete time framework, in which major desirable properties of idiosyncratic shocks and random matchings hold. In this framework the agent space constitutes a probability space, and the probability distribution for each agent is replaced by the population distribution. Unlike previous authors, we question the assumption of known identity  the location on the agent space. We assume that the agents only know their previous history  what had happened to them before,  but not their identity. The construction justifies the use of numerous dynamic models of idiosyncratic shocks and random matchings.
Item Type:  MPRA Paper 

Original Title:  A Theory of Continuum Economies with Idiosyncratic Shocks and Random 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:  7445 
Depositing User:  Andrei Karavaev 
Date Deposited:  05. Mar 2008 07:53 
Last Modified:  17. Feb 2013 23:42 
References:  AlNajjar, Nabil I. 2004. "Aggregation and the Law of Large Numbers in Large Economies." Games and Economic Behavior 47, pp. 135. Aliprantis, Charalambos D., G. Camera, and D. Puzzello. 2006. "Matching and Anonymity." Economic Theory 29, pp. 415432. Aliprantis, Charalambos D., G. Camera, and D. Puzzello. 2007. "A Random Matching Theory." Games and Economic Behavior 59, pp. 1–16. AlosFerrer, Carlos. 1999. "Dynamical Systems with a Continuum of Randomly Matched Agents." J. Econ. Theory 86, pp. 245267. AlosFerrer, Carlos. 2002. "Individual Randomness in Economic Models with a Continuum of Agents." Working paper. AlosFerrer, Carlos. 2002. "Random Matching of Several Infinite Populations." Annals of Operations Research 114, pp. 3338. Boylan, Richard T. 1992. "Laws of Large Numbers for Dynamical Systems with Randomly Matched Individuals." J. Econ. Theory 57, pp. 473504. Boylan, Richard T. 1995. "Continuous Approximations of Dynamical Systems with Randomly Matched Individuals." J. Econ. Theory 66, pp. 615625. Doob, J.L.. 1937. "Stochastic processes depending on a continuous parameter." Trans. Am. Math. Soc. 42, 107–140. Duffie, Darrell, and Yeneng Sun. 2004. "The Exact Law of Large Numbers for Independent Random Matching." Working paper, Graduate School of Business, Stanford University. Duffie, Darrell, and Yeneng Sun. 2007. "Existence of Independent Random Matching." Annals of Applied Probability 17, pp. 386419. Feldman, Mark, and Christian Gilles. 1985. "An Expository Note on Individual Risk without Aggregate Uncertainty." J. Econ. Theory 35, pp. 2632. Feller, William. 1968. "An Introduction to Probability Theory and Its Applications." Volume I, Wiley International Edition, New York, 3rd Edition, 510 pp. Gale, Douglas. 1986. "Bargaining and Competition Part I: Characterization." Econometrica 54(4), pp.~785806. Gilboa, Itzhak, and Akihiko Matsui. 1992. "A Model of Random Matching." Journal of Mathematical Economics 21, pp. 185197. Green, Edward J. 1994. "IndividualLevel Randomness in a Nonatomic Population." Working paper, University of Minnesota. Green, Edward J., and Ruilin Zhou. 2002. "Dynamic Monetary Equilibrium in a Random Matching Economy." Econometrica 70, pp. 929969. Halmos, Paul. 1974. "Naive set theory." SpringerVerlag, New York. Judd, Kenneth L. 1985. "The Law of Large Numbers with a Continuum of IID Random Variables." J. Econ. Theory 35, pp. 1925. Kandori, Michihiro. 1992. "Social Norms and Community Enforcement." The Review of Economic Studies 59(1), pp.~6380. Kocherlakota, Narayana R. 1998. "Money Is Memory." Journal of Economic Theory 81, pp.~232251. McLennan, Andrew, and Hugo Sonnenschein. 1991. "Sequential Bargaining as a Noncooperative Foundation for Walrasian Equilibrium." Econometrica 59, pp. 13951424. Shi, Shouyong. 1997. "A Divisible Search Model of Fiat Money." Econometrica 65(1), pp. 75102. Sun, Yeneng. 1998. "A Theory of Hyperfinite Processes: the Complete Removal of Individual Uncertainty via Exact LLN." Journal of Mathematical Economics 29, pp. 419503. Uhlig, Harald. 1996. "A Law of Large Numbers for Large Economies." Economic Theory 8, pp. 4150. Wentzell, Alexander D. 1981. "A Course in the Theory of Stochastic Processes." New York: McGrawHill. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/7445 