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The perfect foresights' assumption revisited : (I) the existence of equilibrium with multiple price expectations

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  • Lionel De Boisdeffre

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

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    Abstract

    Our earlier papers had extend to asymmetric information the classical existence theorems of general equilibrium theory, under the standard assumption that agents had perfect foresights, that is, they knew, ex ante, which price would prevail on each spot market. Common observation suggests, however, that agents more often trade with an un-precise knowledge of future prices. We now let agents anticipate, in each random state, a set of plausible prices, called expectations, endowed with a probability distribution. These expectations are assumed to define a so-called "structure of beliefs", along which agents' expectations sets intersect on each spot market. We introduce a related concept of "correct foresights equilibrium" (CFE), in which equilibrium prices belong to all agents expectations sets. We prove that the existence of a CFE is still characterized by the no-arbitrage condition of finance. This result, which extends our earlier theorems, shows that private information or price uncertainty would not affect the existence but only the value of equilibrium prices and allocations.

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    Bibliographic Info

    Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00354814.

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    Date of creation: Dec 2008
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    Handle: RePEc:hal:cesptp:halshs-00354814

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    Related research

    Keywords: General equilibrium; incomplete markets; existence of equilibrium; asymmetric information.;

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    1. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer, Springer, vol. 38(2), pages 287-293, February.
    2. Monique Florenzano, 1999. "General equilibrium of financial markets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085543, HAL.
    3. Cornet, Bernard & De Boisdeffre, Lionel, 2002. "Arbitrage and price revelation with asymmetric information and incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 393-410, December.
    4. Monique Florenzano, 2008. "General equilibrium," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne b08005, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, Econometric Society, vol. 47(3), pages 655-78, May.
    6. Lionel Boisdeffre, 2007. "No-arbitrage Equilibria with Differential Information: An Existence Proof," Economic Theory, Springer, Springer, vol. 31(2), pages 255-269, May.
    7. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
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