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Caller Number Five and Related Timing Games

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  • Andreas Park
  • Lones Smith

Abstract

There are two varieties of timing games in economics: Having more predecessors helps in a war of attrition and hurts in a pre-emption game. This paper introduces and explores a spanning class with rank-order payoffs} that subsumes both as special cases. We assume a continuous time setting with unobserved actions and complete information, and explore how equilibria of these games capture many economic and social timing phenomena --- shifting between phases of slow and explosive (positive probability) stopping. Inspired by auction theory, we first show how the symmetric Nash equilibria are each equivalent to a different "potential function". This device straightforwardly yields existence and characterization results. The Descartes Rule of Signs, e.g., bounds the number phase transitions. We describe how adjacent timing game phases interact: War of attrition phases are not played out as long as they would be in isolation, but instead are cut short by pre-emptive atoms. We bound the number of equilibria, and compute the payoff and duration of each equilibrium.

Suggested Citation

  • Andreas Park & Lones Smith, 2008. "Caller Number Five and Related Timing Games," Working Papers tecipa-317, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-317
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    Cited by:

    1. Yingyao Hu & Zhongjian Lin, 2018. "Misclassification and the hidden silent rivalry," CeMMAP working papers CWP12/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Gallice, Andrea, 2008. "Preempting versus Postponing: the Stealing Game," MPRA Paper 10256, University Library of Munich, Germany.
    3. Andrea Gallice, 2016. "Optimal stealing time," Theory and Decision, Springer, vol. 80(3), pages 451-462, March.
    4. Barbos, Andrei, 2013. "De-synchronized clocks in preemption games with risky prospects," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 203-216.
    5. Cheung, Yin-Wong & Friedman, Daniel, 2009. "Speculative attacks: A laboratory study in continuous time," Journal of International Money and Finance, Elsevier, vol. 28(6), pages 1064-1082, October.
    6. Henry, Emeric & Ruiz-Aliseda, Francisco, 2012. "Innovation Beyond Patents: Technological Complexity as a Protection against Imitation," CEPR Discussion Papers 8870, C.E.P.R. Discussion Papers.
    7. Seel, Christian & Stracky, Philipp, 2014. "Continuous Time Contests with Private Information," Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100527, Verein für Socialpolitik / German Economic Association.
    8. Levin, Dan & Peck, James, 2008. "Investment dynamics with common and private values," Journal of Economic Theory, Elsevier, vol. 143(1), pages 114-139, November.
    9. Smirnov, Vladimir & Wait, Andrew, 2015. "Innovation in a generalized timing game," International Journal of Industrial Organization, Elsevier, vol. 42(C), pages 23-33.
    10. Philippe Bich & Rida Laraki, 2014. "On the Existence of Approximate Equilibria and Sharing Rule Solutions in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01071678, HAL.
    11. Seel, Christian & Strack, Philipp, 2012. "Continuois Time Contests," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 376, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    12. Philippe Bich & Rida Laraki, 2014. "On the Existence of Approximate Equilibria and Sharing Rule Solutions in Discontinuous Games," Working Papers hal-01071678, HAL.
    13. Seel, Christian & Strack, Philipp, 2013. "Gambling in contests," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2033-2048.
    14. Schotter, Andrew & Yorulmazer, Tanju, 2009. "On the dynamics and severity of bank runs: An experimental study," Journal of Financial Intermediation, Elsevier, vol. 18(2), pages 217-241, April.
    15. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.

    More about this item

    Keywords

    Games of Timing; War of Attrition; Preemption Game.;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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