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

  • Andreas Park

    (Economics Dept., University of Toronto)

  • Lones Smith

    (Dept. of Economics, University of Michigan)

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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File URL: http://cowles.econ.yale.edu/P/cd/d15b/d1554.pdf
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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
Contact details of provider: Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. 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.
  2. Dilip Abreu & Markus K. Brunnermeier, 2002. "Bubbles and crashes," LSE Research Online Documents on Economics 24905, London School of Economics and Political Science, LSE Library.
  3. Paul Klemperer & Jeremy Bulow, 1999. "The Generalized War of Attrition," Game Theory and Information 9901004, EconWPA.
  4. Sahuguet, Nicolas, 2006. "Volunteering for heterogeneous tasks," Games and Economic Behavior, Elsevier, vol. 56(2), pages 333-349, August.
  5. Hendricks, Kenneth & Weiss, Andrew & Wilson, Charles, 1987. "The War of Attrition in Continuous Time with Complete Information," Working Papers 87-03, C.V. Starr Center for Applied Economics, New York University.
  6. 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.
  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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