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The B.E. Journal of Theoretical Economics

Editor-in-Chief: Schipper, Burkhard

Ed. by Fong, Yuk-fai / Peeters, Ronald / Puzzello , Daniela / Rivas, Javier / Wenzelburger, Jan


IMPACT FACTOR 2018: 0.173
5-year IMPACT FACTOR: 0.248

CiteScore 2018: 0.24

SCImago Journal Rank (SJR) 2018: 0.163
Source Normalized Impact per Paper (SNIP) 2018: 0.186

Mathematical Citation Quotient (MCQ) 2018: 0.08

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ISSN
1935-1704
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Timing Games with Irrational Types: Leverage-Driven Bubbles and Crash-Contingent Claims

Hitoshi Matsushima
Published Online: 2019-08-23 | DOI: https://doi.org/10.1515/bejte-2018-0088

Abstract

This study investigates strategic aspect of leverage-driven bubbles from the viewpoint of game theory and behavioral finance. Even if a company is unproductive, its stock price grows up according to an exogenous reinforcement pattern. During the bubble, this company raises huge funds by issuing new shares. Multiple arbitrageurs strategically decide whether to ride the bubble by continuing to purchase shares through leveraged finance.

We demonstrate two models that are distinguished by whether crash-contingent claim, i. e. contractual agreement such that the purchaser of this claim receives a promised monetary amount if and only if the bubble crashes, is available. We show that the availability of this claim deters the bubble; without crash-contingent claim, the bubble emerges and persists long 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.

We formulate these models as specifications of 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 that each player is irrational with a small but positive probability. We then prove that there exists the unique Nash equilibrium; according to it, every player never selects the initial time. By regarding arbitrageurs as players, we give careful conceptualizations that are necessary to interpret timing games as models of leverage-driven bubbles.

Keywords: timing games with irrational types; uniqueness; awareness heterogeneity; leverage-driven bubbles; crash-contingent claim

JEL Classification: C720; C730; D820; G140

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About the article

Published Online: 2019-08-23


This research was supported by a grant-in-aid for scientific research (KAKENHI 21330043, 25285059) from the Japan Society for the Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of the Japanese government. I am grateful to the editor-in-chief, an anonymous referee, and Professor Takashi Ui for their valuable comments. All errors are mine.


Citation Information: The B.E. Journal of Theoretical Economics, Volume 20, Issue 1, 20180088, ISSN (Online) 1935-1704, DOI: https://doi.org/10.1515/bejte-2018-0088.

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