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Multi-Battle Contests

  • Konrad, Kai A.
  • Kovenock, Dan

We study equilibrium in a multistage race in which players compete in a sequence of simultaneous move component contests. Players may win a prize for winning each component contest, as well as a prize for winning the overall race. Each component contest is an all-pay auction with complete information. We characterize the unique equilibrium analytically and demonstrate that it exhibits endogenous uncertainty. Even a large lead by one player does not fully discourage the other player, and each feasible state is reached with positive probability in equilibrium (pervasiveness). Total effort may exceed the value of the prize by a factor that is proportional to the maximum number of stages. Important applications are to war, sports, and R&D contests and the results have empirical counterparts there.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5645.

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Date of creation: Apr 2006
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Handle: RePEc:cpr:ceprdp:5645
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  1. Thomas Hoehn & Stefan Szymanski, 1999. "The Americanization of European football," Economic Policy, CEPR;CES;MSH, vol. 14(28), pages 203-240, 04.
  2. Baye, M. & Kovenock, D. & de Vries, C., 1990. "The All-Pay Auction with Complete Information," Discussion Paper 1990-51, Tilburg University, Center for Economic Research.
  3. Fearon, James D., 1995. "Rationalist explanations for war," International Organization, Cambridge University Press, vol. 49(03), pages 379-414, June.
  4. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1993. "Rigging the Lobbying Process: An Application of the All-Pay Auction," American Economic Review, American Economic Association, vol. 83(1), pages 289-94, March.
  5. Harris, Christopher & Vickers, John, 1987. "Racing with Uncertainty," Review of Economic Studies, Wiley Blackwell, vol. 54(1), pages 1-21, January.
  6. Garfinkel, M.R. & Skaperdas, S., 2000. "Conflict without Misperceptions or Incomplete Information: how the Future Matters," Papers 99-00-11, California Irvine - School of Social Sciences.
  7. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
  8. Moldovanu, Benny & Sela, Aner, 1999. "The Optimal Allocation of Prizes in Contests," Sonderforschungsbereich 504 Publications 99-75, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  9. Baye, M.R. & Kovenock, D., 1993. "The Solution of the Tullock Rent-Seeking Game when R > 2 : Mixed-Strategy Equilibria and Mean Dissipation Rates," Discussion Paper 1993-68, Tilburg University, Center for Economic Research.
  10. Edward P. Lazear & Sherwin Rosen, 1979. "Rank-Order Tournaments as Optimum Labor Contracts," NBER Working Papers 0401, National Bureau of Economic Research, Inc.
  11. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, 03.
  12. Konrad, Kai A. & Kovenock, Dan, 2005. "Equilibrium and Efficiency in the Tug-Of-War," Purdue University Economics Working Papers 1177, Purdue University, Department of Economics.
  13. Che, Yeon-Koo & Gale, Ian, 2000. "Difference-Form Contests and the Robustness of All-Pay Auctions," Games and Economic Behavior, Elsevier, vol. 30(1), pages 22-43, January.
  14. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1999. " The Incidence of Overdissipation in Rent-Seeking Contests," Public Choice, Springer, vol. 99(3-4), pages 439-54, June.
  15. Ellingsen, T., 1990. "Strategic Buyers and the Social Cost of Monopoly," Papers 05-90, Norwegian School of Economics and Business Administration-.
  16. Johannes Hörner & Nicolas Sahuguet, 2011. "A war of attrition with endogenous effort levels," Economic Theory, Springer, vol. 47(1), pages 1-27, May.
  17. Lee, Tom & Wilde, Louis L, 1980. "Market Structure and Innovation: A Reformulation," The Quarterly Journal of Economics, MIT Press, vol. 94(2), pages 429-36, March.
  18. Budd, Christopher & Harris, Christopher & Vickers, John, 1993. "A Model of the Evolution of Duopoly: Does the Asymmetry between Firms Tend to Increase or Decrease?," Review of Economic Studies, Wiley Blackwell, vol. 60(3), pages 543-73, July.
  19. Klumpp, Tilman & Polborn, Mattias K., 2006. "Primaries and the New Hampshire Effect," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 1073-1114, August.
  20. Harris, Christopher & Vickers, John, 1985. "Perfect Equilibrium in a Model of a Race," Review of Economic Studies, Wiley Blackwell, vol. 52(2), pages 193-209, April.
  21. Stefan Szymanski, 2003. "The Economic Design of Sporting Contests," Journal of Economic Literature, American Economic Association, vol. 41(4), pages 1137-1187, December.
  22. Clark, Derek J. & Riis, Christian, 2000. "Allocation efficiency in a competitive bribery game," Journal of Economic Behavior & Organization, Elsevier, vol. 42(1), pages 109-124, May.
  23. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1993. "The Solution to the Tullock Rent-Seeking Game when r>2: Mixed-Strategy Equilibria and Mean Dissipation Rates," Purdue University Economics Working Papers 1039, Purdue University, Department of Economics.
  24. repec:dgr:uvatin:19970045 is not listed on IDEAS
  25. Fudenberg, Drew & Gilbert, Richard & Stiglitz, Joseph & Tirole, Jean, 1983. "Preemption, leapfrogging and competition in patent races," European Economic Review, Elsevier, vol. 22(1), pages 3-31, June.
  26. Leininger, Wolfgang, 1991. "Patent competition, rent dissipation, and the persistence of monopoly: The role of research budgets," Journal of Economic Theory, Elsevier, vol. 53(1), pages 146-172, February.
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