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Caller Number Five: Timing Games that Morph from One Form to Another

Author

Listed:
  • Andreas Park

    (Economics Dept., University of Toronto)

  • Lones Smith

    (Dept. of Economics, University of Michigan)

Abstract

There are two varieties of timing games in economics: In a war of attrition, more predecessors helps; in a pre-emption game, more predecessors hurts. In this paper, we introduce and explore a spanning class with rank-order payoffs that subsumes both as special cases. In this environment with unobserved actions and complete information, there are endogenously-timed phase transition moments. We identify equilibria with a rich enough structure to capture a wide array of economic and social timing phenomena -- shifting between phases of smooth and explosive entry. We introduce a tractable general theory of this class of timing games based on potential functions. This not only yields existence by construction, but also affords rapid characterization results. We then flesh out the simple economics of phase transitions: Anticipation of later timing games influences current play -- swelling pre-emptive atoms and truncating wars of attrition. We also bound the number of phase transitions as well as the number of symmetric Nash equilibria. Finally, we compute the payoff and duration of each equilibrium, which we uniformly bound. We contrast all results with those of the standard war of attrition.

Suggested Citation

  • Andreas Park & Lones Smith, 2006. "Caller Number Five: Timing Games that Morph from One Form to Another," Cowles Foundation Discussion Papers 1554, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1554
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d15/d1554.pdf
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    References listed on IDEAS

    as
    1. Dilip Abreu & Markus K. Brunnermeier, 2003. "Bubbles and Crashes," Econometrica, Econometric Society, vol. 71(1), pages 173-204, January.
    2. 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 536-556, Autumn.
    3. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    4. Sahuguet, Nicolas, 2006. "Volunteering for heterogeneous tasks," Games and Economic Behavior, Elsevier, vol. 56(2), pages 333-349, August.
    5. 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 663-680, November.
    6. Paul Klemperer & Jeremy Bulow, 1999. "The Generalized War of Attrition," American Economic Review, American Economic Association, vol. 89(1), pages 175-189, March.
    7. 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.
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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. repec:pit:wpaper:233 is not listed on IDEAS
    3. Sahuguet, Nicolas, 2006. "Volunteering for heterogeneous tasks," Games and Economic Behavior, Elsevier, vol. 56(2), pages 333-349, August.
    4. Ochs, Jack & Park, In-Uck, 2010. "Overcoming the coordination problem: Dynamic formation of networks," Journal of Economic Theory, Elsevier, vol. 145(2), pages 689-720, March.
    5. Levin, Dan & Peck, James, 2008. "Investment dynamics with common and private values," Journal of Economic Theory, Elsevier, vol. 143(1), pages 114-139, November.
    6. Brunnermeier, Markus K. & Morgan, John, 2010. "Clock games: Theory and experiments," Games and Economic Behavior, Elsevier, vol. 68(2), pages 532-550, March.
    7. Bo E. Honoré & Aureo de Paula, 2009. ""Interdependent Durations" Third Version," PIER Working Paper Archive 09-039, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Feb 2008.
    8. Steven T. Anderson & Daniel Friedman & Ryan Oprea, 2010. "Preemption Games: Theory and Experiment," American Economic Review, American Economic Association, vol. 100(4), pages 1778-1803, September.
    9. Bo E. Honor & Áureo De Paula, 2010. "Interdependent Durations," Review of Economic Studies, Oxford University Press, vol. 77(3), pages 1138-1163.
    10. Bo E. Honore & Aureo de Paula, 2007. "Interdependent Durations, Second Version," PIER Working Paper Archive 08-044, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Nov 2008.

    More about this item

    Keywords

    timing game; war of attrition; pre-emption game; potential function; Nash equilibrium;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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