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The Generalized War of Attrition

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Author Info
Jeremy I. Bulow (Yale University & Stanford Business School)
Paul Klemperer (Nuffield College, Oxford University)

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Abstract

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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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1142.

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Length: 24 pages
Date of creation: Dec 1996
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Handle: RePEc:cwl:cwldpp:1142

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Related research
Keywords: War of attrition; auctions; standards; natural monopoly; oligopoly; "twoness; " strategic independence; " political decision making;

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Find related papers by JEL classification:
D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
O30 - Economic Development, Technological Change, and Growth - - Technological Change - - - General

References listed on IDEAS
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  1. Joseph Farrell and Garth Saloner., 1988. "Coordination through Committees and Markets," Economics Working Papers 8864, University of California at Berkeley.
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  2. Bulow, Jeremy I & Huang, Ming & Klemperer, Paul, 1996. "Toeholds and Takeovers," CEPR Discussion Papers 1486, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  3. Baye, M.R. & Kovenock, D. & De Vries, C., 1992. "The All-Pay Auction with Complete Information," Papers 8-92-1, Pennsylvania State - Department of Economics.
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  4. 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. [Downloadable!] (restricted)
  5. Kornhauser, Lewis & Rubinstein, Ariel & Wilson, Charles, 1989. "Reputation and Patience in the 'War of Attrition.'," Economica, London School of Economics and Political Science, vol. 56(221), pages 15-24, February. [Downloadable!] (restricted)
  6. Casella, Alessandra & Eichengreen, Barry, 1996. "Can Foreign Aid Accelerate Stabilisation?," Economic Journal, Royal Economic Society, vol. 106(436), pages 605-19, May. [Downloadable!] (restricted)
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  7. 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.
  8. 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. [Downloadable!] (restricted)
  9. Farrell, Joseph & Saloner, Garth, 1986. "Standardization and variety," Economics Letters, Elsevier, vol. 20(1), pages 71-74. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  12. Alesina, A. & Drazen, A., 1991. "Why Are Stabilizations Delayed?," Papers 6-91, Tel Aviv - the Sackler Institute of Economic Studies.
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  13. 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. [Downloadable!] (restricted)
  14. Klemperer, P., 1999. "Auction Theory: a Guide to the Literature," Economics Papers 1999-w12, Economics Group, Nuffield College, University of Oxford.
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  15. Jeremy I. Bulow & Paul Klemperer, 1996. "The Generalized War of Attrition," Cowles Foundation Discussion Papers 1142, Cowles Foundation, Yale University. [Downloadable!]
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  16. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-92, June. [Downloadable!] (restricted)
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  17. Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers 452, UCLA Department of Economics. [Downloadable!]
  18. 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. [Downloadable!] (restricted)
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  19. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May. [Downloadable!] (restricted)
  20. Fudenberg, Drew & Tirole, Jean, 1986. "A Theory of Exit in Duopoly," Econometrica, Econometric Society, vol. 54(4), pages 943-60, July. [Downloadable!] (restricted)
  21. Bulow, Jeremy & Klemperer, Paul, 1994. "Rational Frenzies and Crashes," Journal of Political Economy, University of Chicago Press, vol. 102(1), pages 1-23, February. [Downloadable!] (restricted)
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  22. Fudenberg, Drew & Kreps, David M, 1987. "Reputation in the Simultaneous Play of Multiple Opponents," Review of Economic Studies, Blackwell Publishing, vol. 54(4), pages 541-68, October. [Downloadable!] (restricted)
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