Amegashie, J. Atsu (2012): A nested contest: Tullock meets the All-Pay Auction.
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I present a two-player nested contest which is a convex combination of two widely studied contests: the Tullock (lottery) contest and the all-pay auction. A Nash equilibrium exists for all parameters of the nested contest. If and only if the contest is sufficiently asymmetric, then there is an equilibrium in pure strategies. In this equilibrium, individual and aggregate efforts are lower relative to the efforts in a Tullock contest. This leads to the surprising result that if aggregate efforts in the all-pay auction are higher than the aggregate efforts in the Tullock contest, then aggregate efforts in the nested contest may not lie between aggregate efforts in the all-pay auction and aggregate efforts in the Tullock contest. When the contest is symmetric or asymmetric, I find a mixed-strategy equilibrium and describe some properties of the equilibrium distribution function; I also find the equilibrium payoffs and expected bids. When the weight on the all-pay auction component of this nested contest lies in an intermediate range, then there exist multiple non-payoff-equivalent equilibria such that there is an all-pay auction equilibrium as defined in Alcade and Dahm (2010) and another equilibrium which is not an all-pay auction equilibrium; these equilibria cannot be ranked using the Pareto criterion. If the goal of a contest-designer is to reduce aggregate effort (i.e., wasteful rent-seeking efforts), then this nested contest may be better than both the Tullock contest and the all-pay auction.
|Item Type:||MPRA Paper|
|Original Title:||A nested contest: Tullock meets the All-Pay Auction|
|Keywords:||all-pay auction; discontinuous games; mixed strategy; pure strategy; Tullock contest|
|Subjects:||B - History of Economic Thought, Methodology, and Heterodox Approaches > B2 - History of Economic Thought since 1925 > B21 - Microeconomics
D - Microeconomics > D4 - Market Structure, Pricing, and Design > D44 - Auctions
D - Microeconomics > D7 - Analysis of Collective Decision-Making > D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
|Depositing User:||J. Atsu Amegashie|
|Date Deposited:||01 Oct 2012 11:04|
|Last Modified:||14 Jun 2016 21:57|
Alcalde, J., and Dahm, M. (2007). Tullock and Hirshleifer: a meeting of the minds. Review of Economic Design 11: 101-124.
Alcalde, J., and Dahm, M. (2008). All-pay auction equilibria in contests. Working Paper #4-2008. Department of Economics, University Rovira i Virgili. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1120292
Alcalde, J., and Dahm, M. (2010). Rent seeking and rent dissipation: a neutrality result. Journal of Public Economics 94:1-7.
Amegashie, J. A. (2002). Committees and rent-seeking effort under probabilistic voting. Public Choice 112: 345-350.
Amegashie, J.A. (2006). The 2002 winter Olympics scandal: rent-seeking and committees. Social Choice and Welfare 26: 183-189.
Amegashie, J. A. (2009). American Idol: should it be a singing contest or a popularity contest? Journal of Cultural Economics 33: 265-277.
Baye, M.R., Kovenock, D., and De Vries, C.G. (1993). Rigging the lobbying process: an application of the all-pay auction. American Economic Review 83: 289-294.
Baye, M.R., Kovenock, D., and De Vries, C.G. (1994). The solution to the Tullock rent-seeking game when R > 2: Mixed-strategy equilibria and mean dissipation rates. Public Choice 81: 363-380.
Baye, M.R., Kovenock, D., de Vries, C.G. (1996). The all-pay auction with complete information. Economic Theory 8: 291–305.
Che, Y-K., and Gale, I. (2000). Difference-form contests and the robustness of all-pay auctions. Games and Economic Behavior 30: 22-43.
Chowdhury, S., and Sheremeta, R.M. (2011). Multiple equilibria in Tullock contests. Economics Letters 112: 216-219.
Clark, D., and Riis, C. (1996). On the win probability in rent-seeking games. Mimeo, Department of Economics, University of Oslo, Norway: http://web.bi.no:8000/MCFileManager/files/InstSamfunnsokonomi/rentseekiing.pdf
Congleton, R.D. (1984). Committees and rent-seeking effort. Journal of Public Economics 25: 197-209.
Congleton, R.D, Hillman, A.L., Konrad, K.A. (Eds.), 2008a. 40 Years of Research on Rent Seeking 1: Theory of Rent Seeking. Springer, Heidelberg.
Congleton, R.D, Hillman, A.L., Konrad, K.A. (Eds.), 2008b. 40 Years of Research on Rent Seeking 2 - Applications: Rent Seeking in Practice. Springer, Heidelberg.
Corchon, L., and Dahm, M. (2010). Foundations for contest success functions. Economic Theory 43: 81-98.
Dasgupta, P., and Maskin, E. (1986). The existence of equilibrium in discontinuous games, I: theory. Review of Economic Studies 53: 1-26.
Epstein, G.S., Milchtaich, I., Nitzan, S., and Mordechai, S.E. (2007). Ambiguous political power and contest efforts. Public Choice 132: 113-123
Epstein, G.S., Y. Mealem, and Nitzan, S. (2011). Political culture and discrimination in contests. Journal of Public Economics 2: 88–93.
Epstein, G.S., and Nitzan, S. (2006a). The politics of randomness. Social Choice and Welfare 27: 423-433.
Epstein, G.S., and Nitzan, S. (2006b). Reduced prizes and increased efforts in contests. Social Choice and Welfare 26: 447-453.
Ewerhart, C. (2012). Log-supermodular contests. University of Zurich, mimeo: http://www.eea-esem.com/files/papers/eea-esem/2012/2754/paper.pdf
Fang, H. (2002). Lottery versus all-pay auction models of lobbying. Public Choice 112: 351–371.
Franke, J., Kanzow, C., Leininger, W., and Schwartz, A. (2012). Lottery versus all-pay auction contests: a revenue dominance theorem. Ruhr Economic Papers #315, Technische Universitat Dortmund.
Fu, Q., and Lu, J. (2012) A micro-foundation for generalized multi-prize contests: a noisy ranking perspective. Social Choice and Welfare 38: 497-517.
Hillman, A., and Riley, J.G. (1989). Politically contestable rents and transfers. Economics and Politics 1: 17-39.
Janis, I. (1972) Victims of groupthink: psychological studies of policy decisions and fiascoes. Boston, MA: Houghton Mifflin Company.
Jia, H. (2008). A stochastic derivation of the ratio form of contest success functions. Public Choice 135: 125–130.
Jia, H., and Skaperdas, S. (2011). Technologies of conflict, Chapter 19 in M. R. Garfinkel and S. Skaperdas, eds., Oxford Handbook of the Economics of Peace and Conflict, Oxford University Press.
Jia, H., Skaperdas, S., and Vaidya, S. (2011). Contest functions: theoretical foundations and issues in estimation. International Journal of Industrial Organization, forthcoming.
Konrad, K. (2009). Strategy and dynamics in contests: London School of Economics Perspectives in Economic Analysis. Oxford University Press. Nitzan, S. (1994). Modelling rent-seeking contests. European Journal of Political Economy 10: 41-60. Nti, K.O. (1999). Rent seeking with asymmetric valuations. Public Choice 98: 415-430.
Polishchuk, L., and Tonis, A. (2012). Endogenous contest success functions: a mechanism design approach. Economic Theory, forthcoming.
Siegel, R. (2009). All-pay contests. Econometrica 77: 7