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

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1554.

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Length: 21 pages
Date of creation: Jan 2006
Date of revision:
Publication status: Published in Theoretical Economics (June 2008), 3(2): 231-256
Handle: RePEc:cwl:cwldpp:1554

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Related research

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

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References

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  1. Sahuguet, Nicolas, 2006. "Volunteering for heterogeneous tasks," Games and Economic Behavior, Elsevier, vol. 56(2), pages 333-349, August.
  2. Jeremy Bulow & Paul Klemperer, 1997. "The Generalized War of Attrition," NBER Working Papers 5872, National Bureau of Economic Research, Inc.
  3. 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.
  4. Markus K Brunnermeier, 2002. "Bubbles and Crashes," FMG Discussion Papers dp401, Financial Markets Group.
  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 663-80, November.
  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. 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. Andrea Gallice, 2012. "Preempting versus Postponing: the Stealing Game," Carlo Alberto Notebooks 281, Collegio Carlo Alberto.
  2. Ochs, Jack & Park, In-Uck, 2004. "Overcoming the Coordination Problem: Dynamic Formation of Networks," CEI Working Paper Series 2004-18, Center for Economic Institutions, Institute of Economic Research, Hitotsubashi University.
  3. Levin, Dan & Peck, James, 2008. "Investment dynamics with common and private values," Journal of Economic Theory, Elsevier, vol. 143(1), pages 114-139, November.
  4. Brunnermeier, Markus K & Morgan, John, 2006. "Clock Games: Theory and Experiments," Competition Policy Center, Working Paper Series qt9c11m09n, Competition Policy Center, Institute for Business and Economic Research, UC Berkeley.
  5. Anderson, Steven T & Friedman, Daniel & Oprea, Ryan, 2008. "Preemption Games: Theory and Experiment," Santa Cruz Department of Economics, Working Paper Series qt0pr4g8h1, Department of Economics, UC Santa Cruz.
  6. Bo E. Honor & �ureo De Paula, 2010. "Interdependent Durations," Review of Economic Studies, Oxford University Press, vol. 77(3), pages 1138-1163.
  7. Sahuguet, Nicolas, 2006. "Volunteering for heterogeneous tasks," Games and Economic Behavior, Elsevier, vol. 56(2), pages 333-349, August.
  8. 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.
  9. 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.
  10. Jack Ochs, 2006. "Dynamic Network Formation," Working Papers 233, University of Pittsburgh, Department of Economics, revised Jan 2006.

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