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Ex ante versus interim rationality and the existence of bubbles


  • Barton L. Lipman

    (Department of Economics, Queen's University, Kingston, Ontario K7L 3N6, CANADA)

  • Sugato Bhattacharyya

    (Department of Finance, School of Business, University of Michigan, Ann Arbor, MI 48109, USA)


Tirole (1982) is commonly interpreted as proving that bubbles are impossible with finitely many rational traders with common priors. We study a simple variation of his model in which bubbles can occur, even though traders have common priors and common knowledge that the asset has no fundamental value. In equilibrium, agents purchase the asset at successively higher prices until the bubble "bursts" and no subsequent trade occurs. Each trader's initial wealth determines the last date at which he could possibly trade. The date at which the bubble bursts is a function of these finite "truncation dates" for the individual traders. Since initial wealth is private information, no trader knows when the bubble will burst. There are two key differences between our model and Tirole's which enable us to construct equilibrium bubbles this way. First, Tirole requires ex ante optimality, while we only require every trader's strategy to be optimal conditional on his information-i.e., interim optimal. As we argue in the text, this would seem to be the relevant definition of optimality. Second, Tirole considers competitive equilibria, while we analyze a simple bargaining game.

Suggested Citation

  • Barton L. Lipman & Sugato Bhattacharyya, 1995. "Ex ante versus interim rationality and the existence of bubbles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(3), pages 469-494.
  • Handle: RePEc:spr:joecth:v:6:y:1995:i:3:p:469-494 Note: Received: April 14, 1992; revised version August 24, 1994

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    Cited by:

    1. Muendler, Marc-Andreas, 2008. "Risk-neutral investors do not acquire information," Finance Research Letters, Elsevier, vol. 5(3), pages 156-161, September.
    2. Morris, Stephen & Skiadas, Costis, 2000. "Rationalizable Trade," Games and Economic Behavior, Elsevier, vol. 31(2), pages 311-323, May.
    3. Ahmed, Ehsan & Barkley Rosser, J. Jr. & Uppal, Jamshed Y., 1999. "Evidence of nonlinear speculative bubbles in pacific-rim stock markets," The Quarterly Review of Economics and Finance, Elsevier, vol. 39(1), pages 21-36.
    4. Baye, Michael R. & Kovenock, Dan & de Vries, Casper G., 2012. "The Herodotus paradox," Games and Economic Behavior, Elsevier, vol. 74(1), pages 399-406.
    5. Ehsan Ahmed & Honggang Li & J. Barkley Rosser, 2006. "Nonlinear bubbles in Chinese Stock Markets in the 1990s," Eastern Economic Journal, Eastern Economic Association, vol. 32(1), pages 1-18, Winter.
    6. Felipe Zurita, 2004. "Essays on Speculation," Levine's Working Paper Archive 618897000000000849, David K. Levine.
    7. Ngai-Ching Wong & Man-Chung Ng, 2004. "The No Trade Principle in General Environments," Econometric Society 2004 Far Eastern Meetings 630, Econometric Society.
    8. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    9. Lehrer, Ehud & Samet, Dov, 2014. "Belief consistency and trade consistency," Games and Economic Behavior, Elsevier, vol. 83(C), pages 165-177.
    10. Bhattacharya, Utpal, 2003. "The optimal design of Ponzi schemes in finite economies," Journal of Financial Intermediation, Elsevier, vol. 12(1), pages 2-24, January.

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    JEL classification:

    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L22 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Organization and Market Structure
    • L68 - Industrial Organization - - Industry Studies: Manufacturing - - - Appliances; Furniture; Other Consumer Durables


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