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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 Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1187.

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Length: 33 pages
Date of creation: Mar 2006
Date of revision:
Handle: RePEc:pur:prukra:1187
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  1. 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.
  2. Michael R. Baye & Dan Kovenock & Casper G. de Vries, 1997. "The Incidence of Overdissipation in Rent-Seeking Contests," Tinbergen Institute Discussion Papers 97-045/2, Tinbergen Institute.
  3. Michelle R Garfinkel & Stergios Skaperdas, 2001. "Conflict Without Misperceptions or Incomplete Information: How the Future Matters," Levine's Working Paper Archive 563824000000000011, David K. Levine.
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  7. 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.
  8. Edward P. Lazear & Sherwin Rosen, 1979. "Rank-Order Tournaments as Optimum Labor Contracts," NBER Working Papers 0401, National Bureau of Economic Research, Inc.
  9. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer, vol. 8(2), pages 291-305.
  10. Stefan Szymanski, 2003. "The Economic Design of Sporting Contests," Journal of Economic Literature, American Economic Association, vol. 41(4), pages 1137-1187, December.
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  13. 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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  17. Thomas Hoehn & Stefan Szymanski, 1999. "The Americanization of European football," Economic Policy, CEPR;CES;MSH, vol. 14(28), pages 203-240, 04.
  18. 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.
  19. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
  20. Fearon, James D., 1995. "Rationalist explanations for war," International Organization, Cambridge University Press, vol. 49(03), pages 379-414, June.
  21. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
  22. Christopher Harris & John Vickers, 1985. "Perfect Equilibrium in a Model of a Race," Review of Economic Studies, Oxford University Press, vol. 52(2), pages 193-209.
  23. Christopher Budd & Christopher Harris & John Vickers, 1993. "A Model of the Evolution of Duopoly: Does the Asymmetry between Firms Tend to Increase or Decrease?," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 543-573.
  24. Che,Y.K. & Gale,I., 1998. "Difference-form contests and the robustness of all-pay auctions," Working papers 6, Wisconsin Madison - Social Systems.
  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.
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