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Circumventing the Hart Puzzle

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Abstract
The paper demonstrates the existence of sequential equilibria in a pure exchange economy, where asymmetrically informed agents exchange consumption goods and securities of all kinds, on incomplete markets. Standard models rely on Radner's (1972, 1979) rational expectation assumptions, along which agents know the maps between the information signals, the states of nature and the equilibrium prices. As shown by Hart (1975), equilibrium may then fail to exist, even when agents have symmetric information and smooth preferences. In that setting, Duffie-Shafer (1985) shows from differential topology arguments, that interior equilibria exist generically. The current paper proceeds differently. It drops rational expectations to allow for an infinitesimal uncertainty over future spot prices. This device permits to circumvent Hart's 1975 problem, without using differential topology. Then, the paper shows that a generic condition on payoffs and forecasts guarantees the exostence of equilibria. It is consistent with non-transitive preferences, non-interior consumptions, asymmetric information and normalized spot prices at equilibrim. It also serves to prove existence in a more general model, which drops Radner's rational expectations

Suggested Citation

  • Lionel de Boisdeffre, 2018. "Circumventing the Hart Puzzle," Documents de travail du Centre d'Economie de la Sorbonne 18027, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:18027
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2018/18027.pdf
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    References listed on IDEAS

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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. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
    3. Kurz, Mordecai, 1994. "On the Structure and Diversity of Rational Beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 877-900, October.
    4. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    5. Duffie, Darrell & Shafer, Wayne, 1986. "Equilibrium in incomplete markets: II : Generic existence in stochastic economies," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 199-216, June.
    6. Gale, D. & Mas-Colell, A., 1979. "Corrections to an equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 297-298, December.
    7. Kurz, Mordecai, 1994. "On Rational Belief Equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 859-876, October.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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    More about this item

    Keywords

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

    JEL classification:

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

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