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Existence of an equilibrium for infinite horizon economies with and without complete information

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  • Raad, R.

Abstract

This work proves the existence of an equilibrium for an infinite horizon economy where trade takes place sequentially over time. There exist two types of agents: the first correctly anticipates all future contingent endogenous variables with complete information as in Radner [Radner, R. (1972). Existence of equilibrium of plans, prices and price expectations in a sequence of markets. Econometrica, 289–303] and the second has exogenous expectations about the future environment as in Grandmont [Grandmont, J. M. (1977). Temporary general equilibrium theory. Econometrica, 535–572] and information based on the current and past aggregate variables including those which are private knowledge. Agents with exogenous expectations may have inconsistent optimal plans but have predictive beliefs in the context of Blackwell and Dubbins [Blackwell, D., Dubins, L. (1962). Merging of opinions with increasing information. The Annals of Mathematical Statistics, 882–886] with probability transition rules based on all observed variables. We provide examples of this framework applied to models of differential information and environments exhibiting results of market selection and convergence of an equilibrium. The existence result can be used to conclude that, by adding the continuity assumption on the probability transition rules, we obtain the existence of an equilibrium for some models of differential information and incomplete markets.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 48 (2012)
Issue (Month): 4 ()
Pages: 247-262

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Handle: RePEc:eee:mateco:v:48:y:2012:i:4:p:247-262

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: General equilibrium; Endogenous uncertainty; Perfect foresight; Market selection; Differential information; Incomplete markets;

References

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  1. Magill, M. & Quinzii, M., 1992. "Infinite Horizon Incomplete Markets," DELTA Working Papers, DELTA (Ecole normale supérieure) 92-26, DELTA (Ecole normale supérieure).
  2. Wassim Daher & V. Filipe Martins-Da-Rocha & Yiannis Vailakis, 2005. "Asset market equilibrium with short-selling and differential information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00173787, HAL.
  3. Lawrence Blume & David Easley, 2006. "If You're so Smart, why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Econometrica, Econometric Society, Econometric Society, vol. 74(4), pages 929-966, 07.
  4. Hellwig, Martin F., 1996. "Sequential decisions under uncertainty and the maximum theorem," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 25(4), pages 443-464.
  5. Hervés-Beloso, Carlos & Martins-da-Rocha, Victor Filipe & Monteiro, Paulo Klinger, 2008. "Equilibrium theory with asymmetric information and infinitely many states," Economics Working Papers (Ensaios Economicos da EPGE) 673, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  6. Luciano Castro & Marialaura Pesce & Nicholas Yannelis, 2011. "Core and equilibria under ambiguity," Economic Theory, Springer, Springer, vol. 48(2), pages 519-548, October.
  7. Allen, Beth E, 1981. "Generic Existence of Completely Revealing Equilibria for Economies with Uncertainty when Prices Convey Information," Econometrica, Econometric Society, Econometric Society, vol. 49(5), pages 1173-99, September.
  8. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, Econometric Society, vol. 40(2), pages 289-303, March.
  9. Grandmont, Jean-Michel, 1977. "Temporary General Equilibrium Theory," Econometrica, Econometric Society, Econometric Society, vol. 45(3), pages 535-72, April.
  10. Jordan, J S, 1977. "The Continuity of Optimal Dynamic Decision Rules," Econometrica, Econometric Society, Econometric Society, vol. 45(6), pages 1365-76, September.
  11. Raad, Rodrigo Jardim, 2011. "Exogenous expectations on endogenous uncertainty: recursive equilibrium and survival," Economics Working Papers (Ensaios Economicos da EPGE) 715, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  12. Stigum, Bernt P, 1969. "Competitive Equilibria under Uncertainty," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 83(4), pages 533-61, November.
  13. Svensson, Lars E O, 1981. "Efficiency and Speculation in a Model with Price-Contingent Contracts," Econometrica, Econometric Society, Econometric Society, vol. 49(1), pages 131-51, January.
  14. Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, Econometric Society, vol. 68(6), pages 1303-1342, November.
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