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Caller Number Five and related timing games

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Author Info

  • Park, Andreas

    ()
    (Department of Economics, University of Toronto)

  • Smith, Lones

    ()
    (Department of Economics, University of Michigan)

Abstract

There are two varieties of timing games in economics: wars of attrition, in which having more predecessors helps, and pre-emption games, in which having more predecessors hurts. This paper introduces and explores a spanning class with rank-order payoffs that subsumes both varieties as special cases. We assume time is continuous, actions are unobserved, and information is complete, and explore how equilibria of the games, in which there is shifting between phases of slow and explosive (positive probability) stopping, capture many economic and social timing phenomena. Inspired by auction theory, we first show how each symmetric Nash equilibrium is equivalent to a different "potential function.'' By using this function, we straightforwardly obtain existence and characterization results. Descartes' Rule of Signs bounds the number of 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.

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Bibliographic Info

Article provided by Econometric Society in its journal Theoretical Economics.

Volume (Year): 3 (2008)
Issue (Month): 2 (June)
Pages:

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Handle: RePEc:the:publsh:375

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Web page: http://econtheory.org

Related research

Keywords: Games of timing; war of attrition; preemption game;

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References

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  1. Rida Laraki & Eilon Solan & Nicolas Vieille, 2003. "Continuous-time Games of Timing," Discussion Papers 1363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer, vol. 8(2), pages 291-305.
  3. Sahuguet, Nicolas, 2006. "Volunteering for heterogeneous tasks," Games and Economic Behavior, Elsevier, vol. 56(2), pages 333-349, August.
  4. Dilip Abreu & David G. Pearce, 2006. "Reputational Wars of Attrition with Complex Bargaining Postures," Levine's Working Paper Archive 122247000000001218, David K. Levine.
  5. Paul Klemperer & Jeremy Bulow, 1999. "The Generalized War of Attrition," American Economic Review, American Economic Association, vol. 89(1), pages 175-189, March.
  6. McLennan, A., 1999. "The Expected Number of Nash Equilibria of a Normal Form Game," Papers 306, Minnesota - Center for Economic Research.
  7. Michael Ostrovsky & Michael Schwarz, 2006. "Synchronization under uncertainty," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(1), pages 1-16.
  8. Levin, Dan & Peck, James, 2003. " To Grab for the Market or to Bide One's Time: A Dynamic Model of Entry," RAND Journal of Economics, The RAND Corporation, vol. 34(3), pages 536-56, Autumn.
  9. Shinkai, Tetsuya, 2000. "Second Mover Disadvantages in a Three-Player Stackelberg Game with Private Information," Journal of Economic Theory, Elsevier, vol. 90(2), pages 293-304, February.
  10. Bouis, R. & Huisman, K.J.M. & Kort, P.M., 2006. "Investment in Oligopoly under Uncertainty: The Accordion Effect," Discussion Paper 2006-69, Tilburg University, Center for Economic Research.
  11. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  12. Dilip Abreu & Markus K. Brunnermeier, 2003. "Bubbles and Crashes," Econometrica, Econometric Society, vol. 71(1), pages 173-204, January.
  13. Hendricks, Ken & Weiss, Andrew & Wilson, Charles A, 1988. "The War of Attrition in Continuous Time with Complete Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 663-80, November.
  14. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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Citations

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Cited by:
  1. Gallice, Andrea, 2008. "Preempting versus Postponing: the Stealing Game," MPRA Paper 10256, University Library of Munich, Germany.
  2. 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.
  3. 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.
  4. Francisco Ruiz Aliseda & Emeric Henry, 2013. "Innovation beyond Patents: Technological Complexity as a Protection against Imitation," Sciences Po Economics Discussion Papers 2013-06, Sciences Po Departement of Economics.
  5. Dan Levin & James Peck, 2005. "Investment Dynamics with Common and Private Values," Levine's Bibliography 666156000000000607, UCLA Department of Economics.
  6. 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.
  7. Barbos, Andrei, 2012. "De-synchornized Clocks in Preemption Games with Risky Prospects," MPRA Paper 40846, University Library of Munich, Germany.
  8. Smirnov, Vladimir & Wait, Andrew, 2013. "Innovation in a generalized timing game," Working Papers 2013-16, University of Sydney, School of Economics.
  9. Seel, Christian & Strack, Philipp, 2013. "Gambling in contests," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2033-2048.
  10. Seel, Christian & Strack, Philipp, 2012. "Gambling in Contests," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 375, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.

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