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Ex ante versus Interim Rationality and the Existence of Bubbles

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  • Bhattacharyya, Sugato
  • Lipman, Barton L

Abstract

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 even though it is common knowledge that the asset has no fundamental value at all. In the equilibria we construct agents purchase the asset at successively higher prices (in expectation) until the bubble "bursts" and no subsequent trade occurs. In equilibrium, each trader has a finite "truncation date" and the date at which the bubble bursts is a function of these. Since no trader knows everyone's truncation date, none knows when the bubble will burst. As we show, these random truncations can arise from extrinsic uncertainty (i.e. sunspots) or intrinsic uncertainty (such as uncertainty regarding the initial wealth of other traders). There are two key differences between our model and Tirole's which enable us to use this device to construct equilibrium bubble. First, Tirole requires ex ante optimality, while we only require every trader's strategy to be optimal conditional on his information (specifically, on his truncation date)--i.e., interim optimal. Since each trader knows his information before he actually trades, this would seem to be the relevant definition of optimality. Second, Tirole considers rational expectations equilibria, while we analyze a demand submission game.
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Suggested Citation

  • Bhattacharyya, Sugato & Lipman, Barton L, 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, November.
  • Handle: RePEc:spr:joecth:v:6:y:1995:i:3:p:469-94
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    Cited by:

    1. Baye, Michael R. & Kovenock, Dan & de Vries, Casper G., 2012. "The Herodotus paradox," Games and Economic Behavior, Elsevier, vol. 74(1), pages 399-406.
    2. Felipe Zurita, 2004. "Essays on Speculation," Levine's Working Paper Archive 618897000000000849, David K. Levine.
    3. Jason Shachat & J. Todd Swarthout, 2010. "Procurement Auctions for Differentiated Goods," Decision Analysis, INFORMS, vol. 7(1), pages 6-22, March.
    4. Muendler, Marc-Andreas, 2008. "Risk-neutral investors do not acquire information," Finance Research Letters, Elsevier, vol. 5(3), pages 156-161, September.
    5. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    6. Morris, Stephen & Skiadas, Costis, 2000. "Rationalizable Trade," Games and Economic Behavior, Elsevier, pages 311-323.
    7. Lehrer, Ehud & Samet, Dov, 2014. "Belief consistency and trade consistency," Games and Economic Behavior, Elsevier, vol. 83(C), pages 165-177.
    8. 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.
    9. 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.
    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.

    More about this item

    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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