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Sequential all-pay auctions with noisy outputs. (English) Zbl 1284.91192
Summary: We study a sequential all-pay auction with two contestants who are privately informed about a parameter (ability) that affects their cost of effort. Contestant 1 (the first mover) exerts an effort in the first period which translates into an observable output, but with some noise, and contestant 2 (the second mover) observes this noisy output. Then, contestant 2 exerts an effort in the second period, and wins the contest if her output is larger than or equal to the observed noisy output of contestant 1; otherwise, contestant 1 wins. We study two variations of this model: one in which both contestants do not know the realization of the noise when they exert their effort (symmetric information), and another in which contestant 1 knows the realization of the noise when exerting her effort, while contestant 2 does not (asymmetric information). For both variations, we characterize the subgame perfect equilibrium and examine the effect of a random noise on the contestants’ equilibrium outputs. In particular we show that contestants’ equilibrium behavior in our model is robust to the existence of a small noise.
91B26 Auctions, bargaining, bidding and selling, and other market models
Full Text: DOI
[1] Akerlof, R.; Holden, R., The nature of tournaments, Economic Theory, 51, 289-313, (2012) · Zbl 1262.91101
[2] Amman, E.; Leininger, W., Asymmetric all-pay auctions with incomplete information: the two-player case, Games and Economic Behavior, 14, 1-18, (1996) · Zbl 0860.90040
[3] Baye, M.; Kovenock, D.; de Vries, C., The all-pay auction with complete information, Economic Theory, 8, 291-305, (1996) · Zbl 0859.90058
[4] Baye, M.; Kovenock, D.; de Vries, C., Contests with rank-order spillovers, Economic Theory, (2008), (forthcoming) · Zbl 1262.91077
[5] Che, Y. K.; Gale, I., Caps on political lobbying, American Economic Review, 88, 3, 643-651, (1998)
[6] Che, Y. K.; Gale, I., Difference-form contests and the robustness of all-pay auctions, Games and Economic Behavior, 30, 22-43, (2000) · Zbl 0938.91003
[7] Ederer, F., Feedback and motivation in dynamic tournaments, Journal of Economics and Management Strategy, 19, 733-769, (2010)
[8] Gavious, A.; Moldovanu, B.; Sela, A., Bid costs and endogenous bid caps, Rand Journal of Economics, 33, 4, 709-722, (2003)
[9] Hillman, A.; Riley, J., Politically contestable rents and transfers, Economics and Politics, 1, 17-39, (1989)
[10] Krishna, V.; Morgan, J., An analysis of the war of attrition and the all-pay auction, Journal of Economic Theory, 72, 2, 343-362, (1997) · Zbl 0883.90054
[11] Krishna, V.; Morgan, J., The winner-take-all principle in small tournaments, Advances in Applied Microeconomics, 7, 61-74, (1998)
[12] Lazear, E.; Rosen, S., Rank order tournaments as optimum labor contracts, Journal of Political Economy, 89, 841-864, (1981)
[13] Leininger, W., Patent competition, rent dissipation and the persistence of monopoly, Journal of Economic Theory, 53, 1, 146-172, (1991) · Zbl 0717.90021
[14] Moldovanu, B.; Sela, A., The optimal allocation of prizes in contests, American Economic Review, 91, 3, 542-558, (2001)
[15] Moldovanu, B.; Sela, A., Contest architecture, Journal of Economic Theory, 126, 1, 70-97, (2006) · Zbl 1108.91008
[16] Moldovanu, B.; Sela, A.; Shi, X., Carrots and sticks: prizes and punishments in contests, Economic Inquiry, 50, 2, 453-462, (2012)
[17] Nalebuff, B.; Stiglitz, J., Prizes and incentives: towards a general theory of compensation and competition, Bell Journal of Economics, 14, 21-43, (1983)
[18] Rosen, S., Prizes and incentives in elimination tournaments, American Economic Review, 76, 701-715, (1986)
[19] Segev, E., Sela, A., (2011). Sequential all-pay auctions with head starts. Working Paper, Ben-Gurion University. · Zbl 1307.91091
[20] Siegel, R., All-pay contests, Econometrica, 77, 1, 71-92, (2009) · Zbl 1160.91315
[21] Yildirim, H., Contests with multiple rounds, Games and Economic Behavior, 51, 213-227, (2005) · Zbl 1112.91015
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