Bhowmik, Anuj and Cao, Jiling (2015): Rational Expectations Equilibria: Existence and Representation.

PDF
MPRA_paper_63196.pdf Download (156kB)  Preview 
Abstract
In this paper, we continue to explore the equilibrium theory under ambiguity. For a model of a pure exchange and asymmetric information economy with a measure space of agents whose exogenous uncertainty is described by a complete probability space, we establish a representation theorem for a Bayesian or maximin rational expectations equilibrium allocation in terms of a statewise Walrasian equilibrium allocation. This result also strengthens the theorems on the existence and representation of a (Bayesian) rational expectations equilibrium or a maximin rational expectations equilibrium in the literature.
Item Type:  MPRA Paper 

Original Title:  Rational Expectations Equilibria: Existence and Representation 
Language:  English 
Keywords:  Asymmetric information; Bayesian rational expectations equilibrium; Maximin rational expectations equilibrium; Pure exchange economy; Walrasian equilibrium. 
Subjects:  D  Microeconomics > D5  General Equilibrium and Disequilibrium > D51  Exchange and Production Economies D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D82  Asymmetric and Private Information ; Mechanism Design 
Item ID:  63196 
Depositing User:  Jiling Cao 
Date Deposited:  25. Mar 2015 09:52 
Last Modified:  25. Mar 2015 10:27 
References:  [1] C. D. Aliprantis, K. C. Border, Infinite dimensional analysis: A hitchhiker's guide, Third edition, Springer, Berlin, 2006. [2] B. Allen, Generic existence of completely revealing equilibria with uncertainty, when prices convey information, Econometrica 49 (1981), 11731199. [3] B. Allen, Strict rational expectations equilibria with diffuseness, J. Econ. Theory 27 (1982), 2046. [4] L. Angeloni and V. Filipe MartinsdaRocha, Large economies with differential information and without disposal, Econ. Theory 38 (2009), 263286. [5] K. J. Arrow, G. Debreu, Existence of an equilibrium for a competitive economy, Econometrica 22 (1954), 265290. [6] J. P. Aubin, H. Frankowska, Setvalued analysis, Birkhauser, Boston, 1990. [7] R. J. Aumann, Integrals of setvalued functions. J. Math. Anal. Appl. 12 (1965), 112. [8] R. J. Aumann, Existence of competitive equilibria in markets with a continuum of traders, Econometrica 34 (1966), 117. [9] A. Bhowmik, J. Cao, Blocking efficiency in an economy with asymmetric information, J. Math. Econ. 48 (2012), 396403. [10] A. Bhowmik, J. Cao and N. C. Yannelis, Aggregate preferred correspondence and the existence of a maximin REE, J. Math. Anal. Appl. 414 (2014), 2945. [11] G. Debreu, Theory of value: an axiomatic analysis of economic equilibrium, John Wiley & Sons, New York, 1959. [12] L. I. de Castro, M. Pesce, N. C. Yannelis, A new perspective on rational expectations, preprint, 2013. [13] E. Einy, D. Moreno, B. Shitovitz, Rational expectations equilibria and the expost core of an economy with asymmetric information, J. Math. Econ. 34 (2000), 527535. [14] E. Einy, D. Moreno, B. Shitovitz, Competitive and core allocations in large economies with differential information, Econ. Theory 18 (2001), 321332. [15] D. Glycopantis, A. Muir, N. C. Yannelis, Nonimplementation of rational expectations as a perfect Bayesian equilibrium, Econ. Theory 26 (2005), 765791. [16] W. Hildenbrand, Core and equilibria in large economies, Princeton University Press, 1974. [17] C. J. Himmelberg, Measurable relations, Fund. Math. 87 (1975), 5372. [18] D. M. Kreps, A note on `fulfilled expectations' equilibrium, J. Econ. Theory 14 (1977), 3243. [19] L. W. McKenzie, On the existence of general equilibrium for a competitive market, Econometrica 27 (1959), 5471. [20] M. Pesce, On mixed markets with asymmetric information, Econ. Theory 45 (2010), 2353. [21] R. Radner, Competitive equilibrium under uncertainty, Econometrica 36 (1968), 3158. [22] R. Radner, Rational expectation equilibrium: generic existence and information revealed by prices, Econometrica 47 (1979), 655678. [23] S. Shreve, Stochastic calculus for finance II: Continuoustime models, Springer, 2013. [24] Y. Sun, L. Wu and N. C. Yannelis, Existence, incentive compatibility and efficiency of the rational expectations equilibrium, Games Econ. Behav. 76 (2012), 329339. [25] K. Vind, A third remark on the core of an atomless economy, Econometrica 40 (1972), 585586. [26] N. C. Yannelis, The core of an economy with differential information, Econ. Theory 1 (1991), 183197. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/63196 