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Timing Games with Irrational Types: Leverage-Driven Bubbles and Crash-Contingent Claims

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  • Hitoshi Matsushima

    (Faculty of Economics, The University of Tokyo)

Abstract

This study investigates a timing game with irrational types; each player selects a time in a fixed time interval, and the player who selects the earliest time wins the game. We assume the possibility of irrational types in that each player is irrational with a positive probability, thus selecting the terminal time. We show that there exists the unique Nash equilibrium; according to it, every player never selects the initial time. As an application, we analyze a strategic aspect of leverage-driven bubbles; even if a company is unproductive, its stock price grows up according to an exogenous reinforcement pattern. During the bubble, this company is willing to raise huge funds by issuing new shares. We regard players as arbitrageurs, who decide whether to ride the bubble or burst it. We demonstrate two models, which are distinguished by whether crash-contingent claim, i.e., contractual agreement such that the purchaser of this claim receives a promised monetary amount from its seller if and only if the bubble crashes, is available. The availability of this claim deters the bubble; without crash-contingent claim, the bubble emerges and persists even if the degree of reinforcement is insufficient. Without crash-contingent claim, high leverage ratio fosters the bubble, while with crash-contingent claim, it rather deters the bubble.

Suggested Citation

  • Hitoshi Matsushima, 2018. "Timing Games with Irrational Types: Leverage-Driven Bubbles and Crash-Contingent Claims," CIRJE F-Series CIRJE-F-1088, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2018cf1088
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2018/2018cf1088.pdf
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    References listed on IDEAS

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    1. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    2. Ana Fostel & John Geanakoplos, 2012. "Tranching, CDS, and Asset Prices: How Financial Innovation Can Cause Bubbles and Crashes," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(1), pages 190-225, January.
    3. Matsushima, Hitoshi, 2013. "Behavioral aspects of arbitrageurs in timing games of bubbles and crashes," Journal of Economic Theory, Elsevier, vol. 148(2), pages 858-870.
    4. John Geanakoplos, 2009. "The Leverage Cycle," Cowles Foundation Discussion Papers 1715R, Cowles Foundation for Research in Economics, Yale University, revised Jan 2010.
    5. John Geanakoplos, 2010. "Solving the present crisis and managing the leverage cycle," Economic Policy Review, Federal Reserve Bank of New York, vol. 16(Aug), pages 101-131.
    6. John Geanakoplos, 2010. "The Leverage Cycle," NBER Chapters, in: NBER Macroeconomics Annual 2009, Volume 24, pages 1-65, National Bureau of Economic Research, Inc.
    7. John Geanakoplos, 2010. "Solving the Present Crisis and Managing the Leverage Cycle," Cowles Foundation Discussion Papers 1751, Cowles Foundation for Research in Economics, Yale University.
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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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