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Contests with a Stochastic Number of Players

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Author Info
Alexander Matros
Wooyoung Lim
Abstract

We study Tullock's (1980) n-player contest when each player has an independent probability 0 < p 2 individual equilibrium spending as a function of p is single-peaked and satisfies a single-crossing property for any two different numbers of potential players. However, total equilibrium spending is monotonically increasing in p and n. We also demonstrate that ex-post over-dissipation is a feature of the pure-strategy equilibrium in our model. It turns out that if the contest designer can strategically decide whether to reveal the actual number of participating players or not, then the actual number of participants is always revealed.

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Paper provided by University of Pittsburgh, Department of Economics in its series Working Papers with number 323.

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Date of creation: Jul 2007
Date of revision: Sep 2008
Handle: RePEc:pit:wpaper:323

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Related research
Keywords: Contests Stochastic number of players Over-dissipation.

Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Models of Political Processes: Rent-seeking, Elections, Legislatures, and Voting Behavior
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information

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  1. McAfee, R. Preston & McMillan, John, 1987. "Auctions with a stochastic number of bidders," Journal of Economic Theory, Elsevier, vol. 43(1), pages 1-19, October. [Downloadable!] (restricted)
  2. Stefan Szymanski, 2003. "The Economic Design of Sporting Contests," Journal of Economic Literature, American Economic Association, vol. 41(4), pages 1137-1187, December.
  3. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer, vol. 27(3), pages 375-392. [Downloadable!] (restricted)
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  4. Baye, M.R. & Kovenock, D., 1993. "The Solution to the Tullock Rent-Seeking Game When R > 2: Mixed Strategy Equilibria and Mean Dissipation Rates," Papers 9368, Tilburg - Center for Economic Research.
    Other versions:
  5. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October. [Downloadable!] (restricted)
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  6. Thomas Cusack & Amihai Glazer & Kai Konrad, 2007. "Introduction," Economics of Governance, Springer, vol. 8(3), pages 179-179, May. [Downloadable!] (restricted)
  7. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May. [Downloadable!] (restricted)
  8. 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. [Downloadable!]
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  9. Posner, Richard A, 1975. "The Social Costs of Monopoly and Regulation," Journal of Political Economy, University of Chicago Press, vol. 83(4), pages 807-27, August. [Downloadable!] (restricted)
  10. Krueger, Anne O, 1974. "The Political Economy of the Rent-Seeking Society," American Economic Review, American Economic Association, vol. 64(3), pages 291-303, June. [Downloadable!] (restricted)
  11. Roger Myerson & Karl Wärneryd, 2006. "Population uncertainty in contests," Economic Theory, Springer, vol. 27(2), pages 469-474, January. [Downloadable!] (restricted)
  12. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, vol. 94(1), pages 7-45, September. [Downloadable!] (restricted)
    Other versions:
    • Roger B. Myerson, 1997. "Large Poisson Games," Discussion Papers 1189, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  13. Hurley, Terrance M. & Shogren, Jason F., 1998. "Asymmetric information contests," European Journal of Political Economy, Elsevier, vol. 14(4), pages 645-665, November. [Downloadable!] (restricted)
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