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Price revelation and existence of equilibrium in a private belief economy

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  • Lionel de Boisdeffre

    (CATT - Centre d'Analyse Théorique et de Traitement des données économiques - UPPA - Université de Pau et des Pays de l'Adour, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider a pure exchange financial economy, where rational agents, possibly asymmetrically informed, forecast prices privately and, therefore, face "exogenous uncertainty", on the future state of nature, and "endogenous uncertainty" on future prices. At a sequential equilibrium, all agents expect the "true" price as a possible outcome and elect optimal strategies at the first period, which clear on all markets ex post. We introduce no-arbitrage prices and display their revealing properties. Under mild conditions, we show that a sequential equilibrium exists, whatever the financial structure and agents' private information or beliefs. This result suggests that existence problems of standard sequential equilibrium models, following Hart (1975) or Radner (1979), stem from the rational expectation and perfect foresight assumptions, which are both dropped in our model.

Suggested Citation

  • Lionel de Boisdeffre, 2013. "Price revelation and existence of equilibrium in a private belief economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01053471, HAL.
    • Handle: RePEc:hal:cesptp:halshs-01053471
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01053471
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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. 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.
    3. Grandmont, Jean-Michel, 1993. "Temporary general equilibrium theory," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922, Elsevier.
    4. Busch, Lutz-Alexander & Govindan, Srihari, 2004. "Robust nonexistence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 641-645, September.
    5. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    6. 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.
    7. Momi, Takeshi, 2001. "Non-existence of equilibrium in an incomplete stock market economy," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 41-70, February.
    8. 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.
    9. Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, vol. 41(6), pages 1103-1123, November.
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