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Sequential equilibrium without rational expectations of prices: A theorem of full existence

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We consider a pure exchange economy, where agents, typically asymmetrically informed, exchange commodities, on spot markets, and securities of all kinds, on incomplete financial markets with no model of how future prices are determined. They have private characteristics, anticipations and beliefs. We show they face an incompressible uncertainty, represented by a so-called “minimum uncertainty set”, typically adding to the ‘exogenous uncertainty’, on tomorrow's state of nature, an ‘endogenous uncertainty’ on future spot prices, which may depend on every agent's private anticipations today. At equilibrium, all agents expect the ‘true’ price, in each realizable state, as a possible outcome, and elect optimal strategies, ex ante, which clear on all markets, ex post. Our main Theorem states that equilibrium exists as long as agents' prior anticipations, which may be refined from observing markets, embed that minimum uncertainty set. This result is stronger than the classical ones of generic existence, along Radner (1979), or Hart (1975), based on the rational expectations of prices

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  • Lionel de Boisdeffre, 2017. "Sequential equilibrium without rational expectations of prices: A theorem of full existence," Documents de travail du Centre d'Economie de la Sorbonne 17036, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:17036
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    1. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 287-293, February.
    2. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    3. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
    4. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 287-293, February.
    5. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
    6. 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.
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    More about this item

    Keywords

    sequential equilibrium; temporary equilibrium; perfect foresight; existence; rational expectations; financial markets; asymmetric information; arbitrage;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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