Abstract
We apply the environmental equivalence property of Poisson games (Myerson, In Int J Game Theory 27:375–392, 1998b) to show that, in contests in which the number of contestants is a Poisson random variable with at least two expected contestants and a non-increasing return to effort, ex-ante aggregate effort is less than in a corresponding contest wherein the number of participants is equal to the expected number of contestants under uncertainty. Uncertainty about the number of participants in a rent-seeking contest seems natural. With rent-seeking contests attracting socially wasteful investments of effort or scarce resources, uncertainty generates a social benefit.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Münster (2006) also assumed a Binomial distribution of contestants to obtain results regarding contests with an uncertain number of contestants. Notice that a Poisson distribution is the limiting case of a Binominal distribution.
Higgins et al. (1985) find perfect dissipation ex-ante when the number of contestants is determined endogenously.
A detailed computation of \(\tilde{\pi }(n)\) has been carried out in Myerson and Wärneryd (2006).
Szidarovszky and Okuguchi (Szidarovszky & Okuguchi 1997) have showed that monotonicity and concavity of f are sufficient conditions for the existence of a unique symmetric pure interior Nash equilibrium.
References
Higgins, R. S., Shughart II, W. F., & Tollison, R. D. (1985). Efficient rents 2 free entry and efficient rent seeking. Public Choice, 46, 247–258.
Hillman, A. L. (2013). Rent seeking. In M. Reksulak, L. Razzolini, & W. F. Shughart II (Eds.), The Elgar companion to public choice (2nd ed., pp. 307–330). Cheltenham: Edward Elgar.
Hillman, A. L. (2015). Rents and international trade policy. In R. D. Congleton & A. L. Hillman (Eds.), A companion to the political economy of rent seeking (pp. 187–202). Cheltenham: Edward Elgar.
Konrad, K. A. (2009). Strategy and dynamics in contests. Oxford: Oxford University Press.
Lim, W., & Matros, A. (2009). Contests with a stochastic number of players. Games and Economic Behavior, 67, 584–597.
Long, N. V. (2013). The theory of contests: a unified model and review of the literature. European Journal of Political Economy, 32, 161–181. Reprinted. In: Congleton, R. D., & Hillman, A. L. (Eds.) (2015). A companion to the political economy of rent seeking, (pp. 19–52). Cheltenham: Edward Elgar.
Mohlin, E., Östling, R., & Wang, J. T. Y. (2015). Lowest unique bid auctions with population uncertainty. Economics Letters, 134, 53–57.
Münster, J. (2006). Contests with an unknown number of contestants. Public Choice, 129, 353–368.
Myerson, R. B. (1998a). Extended Poisson games and the Condorcet jury theorem. Games and Economic Behavior, 25, 111–131.
Myerson, R. B. (1998b). Population uncertainty and Poisson games. International Journal of Game Theory, 27, 375–392.
Myerson, R. B. (2000). Large Poisson games. Journal of Economic Theory, 94, 7–45.
Myerson, R. B., & Wärneryd, K. (2006). Population uncertainty in contests. Economic Theory, 27, 469–474.
Park, H., Philippopoulos, A., & Vassilatos, V. (2005). Choosing the size of the public sector under rent seeking from state coffers. European Journal of Political Economy, 21, 830–850.
Posner, R. A. (1975). The social costs of monopoly and regulation. Journal of Political Economy, 83, 807–827. Reprinted. In: Congleton, R. D., Hillman, A. L., & Konrad, K. A. (Eds.) (2008). Forty years of research on rent seeking 2—applications: rent seeking in practice, (pp. 45–65). Heidelberg: Springer.
Shughart II, W. F., & Thomas, D. W. (2015). Regulatory rent seeking. In R. D. Congleton & A. L. Hillman (Eds.), A companion to the political economy of rent seeking (pp. 167–186). Cheltenham: Edward Elgar.
Skaperdas, S. (1996). Contest success functions. Economic Theory, 7, 283–290. Reprinted. In: Congleton, R. D., Hillman, A. L., & Konrad, K. A. (Eds.) (2008). Forty years of research on rent seeking 1—the theory of rent seeking, (pp. 263–270). Heidelberg: Springer.
Szidarovszky, F., & Okuguchi, K. (1997). On the existence and uniqueness of pure Nash equilibrium in rent-seeking games. Games and Economic Behavior, 18, 135–140. Reprinted. In: Congleton, R. D., Hillman, A. L., & Konrad, K. A. (Eds.) (2008). Forty years of research on rent seeking 1—the theory of rent seeking, (pp. 271–276). Heidelberg: Springer.
Tullock, G. (1967). The welfare costs of tariffs, monopolies, and theft. Western Economic Journal, 5, 224–232. Reprinted. In: Congleton, R. D., Hillman, A. L., & Konrad, K. A. (Eds.) (2008). Forty years of research on rent seeking 1—the theory of rent seeking, (pp. 43–53). Heidelberg: Springer.
Tullock, G. (1980). Efficient rent seeking. In Buchanan, J. M., Tollison, R. D., & Tullock G. (Eds.), Towards a theory of the rent-seeking society, pp. 97–112. College Station: Texas A&M University Press. Reprinted. In: Congleton, R. D., Hillman, A. L., & Konrad, K. A. (Eds.) (2008). Forty years of research on rent seeking 1—the theory of rent seeking, (pp. 105–120). Heidelberg: Springer.
Acknowledgements
We thank Monika Köppl-Turyna, Heinrich Ursprung, three anonymous referees and the editor of this journal for helpful comments.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest
Rights and permissions
About this article
Cite this article
Kahana, N., Klunover, D. A note on Poisson contests. Public Choice 165, 97–102 (2015). https://doi.org/10.1007/s11127-015-0295-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11127-015-0295-2