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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.

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Bibliographic Info

Paper provided by University of Toronto, Department of Economics in its series Working Papers with number tecipa-317.

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Length: 30 pages
Date of creation: 29 Apr 2008
Date of revision:
Handle: RePEc:tor:tecipa:tecipa-317

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

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References

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  1. Paul Klemperer & Jeremy Bulow, 1997. "The Generalized War of Attrition," Economics Series Working Papers 1998-W01, University of Oxford, Department of Economics.
  2. Bouis, Romain & Huisman, Kuno J.M. & Kort, Peter M., 2009. "Investment in oligopoly under uncertainty: The accordion effect," International Journal of Industrial Organization, Elsevier, vol. 27(2), pages 320-331, March.
  3. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  4. 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.
  5. Baye, M. & Kovenock, D. & Vries, C. de, 1990. "The All-Pay Auction with Complete Information," Discussion Paper 1990-51, Tilburg University, Center for Economic Research.
  6. 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.
  7. Dilip Abreu & Markus K. Brunnermeier, 2003. "Bubbles and Crashes," Econometrica, Econometric Society, vol. 71(1), pages 173-204, January.
  8. McLennan, A., 1999. "The Expected Number of Nash Equilibria of a Normal Form Game," Papers 306, Minnesota - Center for Economic Research.
  9. Laraki, Rida & Solan, Eilon & Vieille, Nicolas, 2005. "Continuous-time games of timing," Journal of Economic Theory, Elsevier, vol. 120(2), pages 206-238, February.
  10. 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.
  11. Sahuguet, Nicolas, 2006. "Volunteering for heterogeneous tasks," Games and Economic Behavior, Elsevier, vol. 56(2), pages 333-349, August.
  12. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  13. 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.
  14. Dilip Abreu & David G. Pearce, 2006. "Reputational Wars of Attrition with Complex Bargaining Postures," Levine's Working Paper Archive 122247000000001218, David K. Levine.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. Gallice, Andrea, 2008. "Preempting versus Postponing: the Stealing Game," MPRA Paper 10256, University Library of Munich, Germany.
  4. Barbos, Andrei, 2013. "De-synchronized clocks in preemption games with risky prospects," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 203-216.
  5. Seel, Christian & Strack, Philipp, 2013. "Gambling in contests," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2033-2048.
  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. Yin-Wong Cheung & Daniel Friedman, 2009. "Speculative Attacks: A Laboratory Study in Continuous Time," Working Papers 072009, Hong Kong Institute for Monetary Research.
  8. Dan Levin & James Peck, 2005. "Investment Dynamics with Common and Private Values," Levine's Bibliography 666156000000000607, UCLA Department of Economics.
  9. 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.
  10. Smirnov, Vladimir & Wait, Andrew, 2013. "Innovation in a generalized timing game," Working Papers 2013-16, University of Sydney, School of Economics.

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