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Dynamic Equilibrium Bunching

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  • Tao Wang

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    (Queen's University)

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    Abstract

    In this paper, we analyze the asymmetric pure strategy equilibria in a dynamic game of pure information externality. Each player receives a private signal and chooses whether and when to invest. In some of the periods, only a subgroup of the players make decisions, which we call bunching, while the rest of the players do not invest regardless of their signals. Bunching is different from herding; it occurs in the first period and recursively until herding takes place or the game runs out of undecided players. We find that any asymmetric pure strategy equilibrium is more efficient than the symmetric mixed strategy equilibrium. When players become patient enough, herding of investment disappears in the most efficient asymmetric pure strategy equilibrium, while the least efficient asymmetric pure strategy equilibrium resembles those in a fixed timing model, producing an exact match when the discount factor is equal to 1. Bunch sizes are shown to be independent of the total number of players; adding more players to the game need not change early players' behavior. All these are unique properties of the asymmetric pure strategy equilibria. We also show that the asymmetric pure strategy equilibria can accommodate small heterogeneities of the players in costs of acquiring signals, discount factors, or degree of risk aversion. In any of these environments, there exists a unique welfare maximizing equilibrium which provides a natural way for the players to coordinate.

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    File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1291.pdf
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    Bibliographic Info

    Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1291.

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    Length: 42 pages
    Date of creation: Nov 2011
    Date of revision:
    Handle: RePEc:qed:wpaper:1291

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    Related research

    Keywords: bunching; herding; endogenous timing; asymmetric equilibrium; information externality;

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    References

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    1. Daniel Sgroi, 2000. "The Right Choice at the Right Time: A Herding Experiment in Endogenous Time," Economics Series Working Papers 2000-W15, University of Oxford, Department of Economics.
    2. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2004. "Social Learning in One-Arm Bandit Problems," Discussion Papers 1396, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Scharfstein, David. & Stein, Jeremy C., 1988. "Herd behavior and investment," Working papers WP 2062-88., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Gale, D. & Chamley, C., 1992. "Information Revelation and Strategic Delay in a Model of Investment," Papers 10, Boston University - Department of Economics.
    5. Naveen Khanna & Richmond D. Mathews, 2011. "Can herding improve investment decisions?," RAND Journal of Economics, RAND Corporation, vol. 42(1), pages 150-174, 03.
    6. Gul, Faruk & Lundholm, Russell, 1995. "Endogenous Timing and the Clustering of Agents' Decisions," Journal of Political Economy, University of Chicago Press, vol. 103(5), pages 1039-66, October.
    7. Jianbo Zhang, 1997. "Strategic Delay and the Onset of Investment Cascades," RAND Journal of Economics, The RAND Corporation, vol. 28(1), pages 188-205, Spring.
    8. Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 797-817, August.
    9. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
    10. Cao, H. Henry & Han, Bing & Hirshleifer, David, 2011. "Taking the road less traveled by: Does conversation eradicate pernicious cascades?," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1418-1436, July.
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