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The Generalized War of Attrition

  • Jeremy I. Bulow

    (Yale University & Stanford Business School)

  • Paul Klemperer

    (Nuffield College, Oxford University)

We generalize the War of Attrition model to allow for N + K firms competing for N prizes. Two special cases are of particular interest. First, if firms continue to pay their full costs after dropping out (as in a standard-setting context), each firm's exit time is independent both of K and of the actions of other players. Second, in the limit in which firms pay no costs after dropping out (as in a natural-oligopoly problem), the field is immediately reduced to N + 1 firms. Furthermore, we have perfect sorting, so it is always the K - 1 lowest-value players who drop out in zero time, even though each player's value is private information to the player. We apply our model to politics, explaining the length of time it takes to collect a winning coalition to pass a bill.

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File URL: http://cowles.econ.yale.edu/P/cd/d11a/d1142.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 1142.

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Length: 24 pages
Date of creation: Dec 1996
Date of revision:
Handle: RePEc:cwl:cwldpp:1142
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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. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
  2. Arye Hillman & Dov Samet, 1987. "Dissipation of contestable rents by small numbers of contenders," Public Choice, Springer, vol. 54(1), pages 63-82, January.
  3. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, 03.
  4. Baye, M.R. & Kovenock, D. & De Varies, C.G., 1990. "The All-Pay Auction With Complete Information," Papers 9051, Tilburg - Center for Economic Research.
  5. Paul Klemperer & Jeremy Bulow, 1999. "The Generalized War of Attrition," Game Theory and Information 9901004, EconWPA.
  6. Jeremy Bulow & Ming Huang & Paul Klemperer, 1999. "Toeholds and Takeovers," Finance 9903005, EconWPA.
  7. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, June.
  8. Alesina, Alberto & Drazen, Allan, 1991. "Why Are Stabilizations Delayed?," American Economic Review, American Economic Association, vol. 81(5), pages 1170-88, December.
  9. Bulow, Jeremy I. & Klemperer, Paul, 1991. "Rational Frenzies and Crashes," CEPR Discussion Papers 593, C.E.P.R. Discussion Papers.
  10. Kennan, John & Wilson, Robert, 1989. "Strategic Bargaining Models and Interpretation of Strike Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages S87-130, Supplemen.
  11. Klemperer, Paul, 1999. "Auction Theory: a Guide to the Literature," CEPR Discussion Papers 2163, C.E.P.R. Discussion Papers.
  12. Bliss, Christopher & Nalebuff, Barry, 1984. "Dragon-slaying and ballroom dancing: The private supply of a public good," Journal of Public Economics, Elsevier, vol. 25(1-2), pages 1-12, November.
  13. Fudenberg, Drew & Tirole, Jean, 1986. "A Theory of Exit in Duopoly," Econometrica, Econometric Society, vol. 54(4), pages 943-60, July.
  14. Joseph Farrell & Garth Saloner, 1988. "Coordination through Committees and Markets," RAND Journal of Economics, The RAND Corporation, vol. 19(2), pages 235-252, Summer.
  15. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
  16. J. Maynard Smith, 2010. "The Theory of Games and Evolution of Animal Conflicts," Levine's Working Paper Archive 448, David K. Levine.
  17. Gul, Faruk & Lundholm, Russell, 1995. "Endogenous Timing and the Clustering of Agents' Decisions," Journal of Political Economy, University of Chicago Press, vol. 103(5), pages 1039-66, October.
  18. John G. Riley & William Samuelson, 1979. "Optimal Auctions," UCLA Economics Working Papers 152, UCLA Department of Economics.
  19. Klepper, Steven & Simons, Kenneth L, 1997. "Technological Extinctions of Industrial Firms: An Inquiry into Their Nature and Causes," Industrial and Corporate Change, Oxford University Press, vol. 6(2), pages 379-460, March.
  20. Taylor, Curtis R, 1995. "Digging for Golden Carrots: An Analysis of Research Tournaments," American Economic Review, American Economic Association, vol. 85(4), pages 872-90, September.
  21. Kornhauser, Lewis A. & Rubinstein, Ariel & Wilson, Charles, 1986. "Reputation and Patience in the “War of Attrition”," Working Papers 86-06, C.V. Starr Center for Applied Economics, New York University.
  22. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  23. Casella, Alessandra & Eichengreen, Barry, 1994. "Can Foreign Aid Accelerate Stabilization?," CEPR Discussion Papers 961, C.E.P.R. Discussion Papers.
  24. Fudenberg, Drew & Kreps, David M, 1987. "Reputation in the Simultaneous Play of Multiple Opponents," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 541-68, October.
  25. Farrell, Joseph & Saloner, Garth, 1986. "Standardization and variety," Economics Letters, Elsevier, vol. 20(1), pages 71-74.
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