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Ex Ante versus Interim rationality and the existence of bubbles

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  • Sugato Bhattacharyya
  • Barton L. Lipman

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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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_851.pdf
File Function: First version 1992
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 851.

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Length: 45 pages
Date of creation: Apr 1992
Date of revision:
Handle: RePEc:qed:wpaper:851

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Cited by:
  1. Lehrer, Ehud & Samet, Dov, 2014. "Belief consistency and trade consistency," Games and Economic Behavior, Elsevier, vol. 83(C), pages 165-177.
  2. Morris, Stephen & Skiadas, Costis, 2000. "Rationalizable Trade," Games and Economic Behavior, Elsevier, vol. 31(2), pages 311-323, May.
  3. Baye, Michael R. & Kovenock, Dan & de Vries, Casper G., 2012. "The Herodotus paradox," Games and Economic Behavior, Elsevier, vol. 74(1), pages 399-406.
  4. Ngai-Ching Wong & Man-Chung Ng, 2004. "The No Trade Principle in General Environments," Econometric Society 2004 Far Eastern Meetings 630, Econometric Society.
  5. Bhattacharya, Utpal, 2003. "The optimal design of Ponzi schemes in finite economies," Journal of Financial Intermediation, Elsevier, vol. 12(1), pages 2-24, January.
  6. 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.
  7. 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.
  8. Felipe Zurita, 2004. "Essays on Speculation," Levine's Working Paper Archive 618897000000000849, David K. Levine.
  9. Muendler, Marc-Andreas, 2008. "Risk-neutral investors do not acquire information," Finance Research Letters, Elsevier, vol. 5(3), pages 156-161, September.
  10. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.

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