Simple equilibria in general contests. (English) Zbl 1497.91017
Summary: We show how symmetric equilibria emerge in general two-player contests in which skill and effort are combined to produce output according to a general production technology and players have skills drawn from different distributions. The model includes the Tullock models [G. Tullock, “Efficient rent seeking”, in: Towards a theory of the rent-seeking society. Texas A&M University Press. 97–112 (1980)] and Lazear and Rosen models [E. P. Lazear and S. Rosen, “Rank-order tournaments as optimum labor contracts”, J. Polit. Econ. 89, 841–864 (1981)] as special cases. Our paper provides intuition regarding how the contest components interact to determine the incentive to exert effort and sheds new light on classic comparative statics results. In particular, we show that more heterogeneity can increase equilibrium effort.
References:
| [1] | Aoyagi, M., Information feedback in a dynamic tournament, Games Econ. Behav., 70, 242-260 (2010) · Zbl 1200.91031 |
| [2] | Auriol, E.; Friebel, G.; Pechlivanos, L., Career concerns in teams, J. Labor Econ., 20, 289-307 (2002) |
| [3] | Bar-Isaac, H.; Lévy, R., Motivating employees through career paths, J. Labor Econ., 40, 95-131 (2022) |
| [4] | Barbieri, S.; Malueg, D. A.; Topolyan, I., The best-shot all-pay (group) auction with complete information, Econ. Theory, 57, 603-640 (2014) · Zbl 1319.91084 |
| [5] | Barut, Y.; Kovenock, D., The symmetric multiple prize all-pay auction with complete information, Eur. J. Polit. Econ., 14, 627-644 (1998) |
| [6] | Baye, M. R.; Kovenock, D.; de Vries, C. G., The all-pay auction with complete information, Econ. Theory, 8, 291-305 (1996) · Zbl 0859.90058 |
| [7] | Bernhardt, D., Strategic promotion and compensation, Rev. Econ. Stud., 62, 315-339 (1995) · Zbl 0829.90042 |
| [8] | Brown, J., Quitters never win: the (adverse) incentive effects of competing with superstars, J. Polit. Econ., 119, 982-1013 (2011) |
| [9] | Chen, K.-P., Sabotage in promotion tournaments, J. Law Econ. Organ., 19, 119-140 (2003) |
| [10] | Chowdhury, S.; Esteve-Gonzalez, P.; Mukherjee, A., Heterogeneity, leveling the playing field, and affirmative action in contests (2019), Working Paper |
| [11] | Chowdhury, S. M.; Gürtler, O., Sabotage in contests: a survey, Public Choice, 164, 135-155 (2015) |
| [12] | Chowdhury, S. M.; Kim, S.-H., “Small, yet beautiful”: reconsidering the optimal design of multi-winner contests, Games Econ. Behav., 104, 486-493 (2017) · Zbl 1393.91076 |
| [13] | Clark, D. J.; Riis, C., On the win probability in rent-seeking games (1996), University of Tromsø: University of Tromsø Norway, Discussion Paper in Economics E4/96 |
| [14] | Clark, D. J.; Riis, C., Competition over more than one prize, Am. Econ. Rev., 88, 276-289 (1998) |
| [15] | Clark, D. J.; Riis, C., Contest success functions: an extension, Econ. Theory, 11, 201-204 (1998) · Zbl 0901.90186 |
| [16] | Cohen, C.; Kaplan, T. R.; Sela, A., Optimal rewards in contests, Rand J. Econ., 39, 434-451 (2008) |
| [17] | Corchón, L.; Dahm, M., Foundations for contest success functions, Econ. Theory, 43, 81-98 (2010) · Zbl 1186.91021 |
| [18] | Cornes, R.; Hartley, R., Asymmetric contests with general technologies, Econ. Theory, 26, 923-946 (2005) · Zbl 1116.91009 |
| [19] | DeVaro, J.; Kauhanen, A., An “opposing responses” test of classic versus market-based promotion tournaments, J. Labor Econ., 34, 747-779 (2016) |
| [20] | DeVaro, J.; Waldman, M., The signaling role of promotions: Further theory and empirical evidence, J. Labor Econ., 30, 91-147 (2012) |
| [21] | Dewatripont, M.; Jewitt, I.; Tirole, J., The economics of career concerns, part I: comparing information structures, Rev. Econ. Stud., 66, 183-198 (1999) · Zbl 0947.91059 |
| [22] | Drugov, M.; Ryvkin, D., Biased contests for symmetric players, Games Econ. Behav., 103, 116-144 (2017) · Zbl 1393.91078 |
| [23] | Drugov, M.; Ryvkin, D., How noise affects effort in tournaments, J. Econ. Theory, 188, Article 105065 pp. (2020) · Zbl 1447.91005 |
| [24] | Drugov, M.; Ryvkin, D., Hunting for the discouragement effect in contests (2021), Working Paper |
| [25] | Fang, D.; Noe, T.; Strack, P., Turning up the heat: the discouraging effect of competition in contests, J. Polit. Econ., 128, 1940-1975 (2020) |
| [26] | Fu, Q.; Lu, J., The beauty of “bigness”: on optimal design of multi-winner contests, Games Econ. Behav., 66, 146-161 (2009) · Zbl 1161.91368 |
| [27] | Fu, Q.; Lu, J., The optimal multi-stage contest, Econ. Theory, 51, 351-382 (2009) · Zbl 1262.91081 |
| [28] | Fu, Q.; Lu, J., Micro foundations of multi-prize lottery contests: a perspective of noisy performance ranking, Soc. Choice Welf., 38, 497-517 (2012) · Zbl 1239.91048 |
| [29] | Fu, Q.; Wu, Z., Contests: Theory and Topics, Oxford Research Encyclopedia of Economics and Finance (2019) |
| [30] | Fu, Q.; Wu, Z., On the optimal design of biased contests, Theor. Econ., 15, 1435-1470 (2020) · Zbl 1466.91073 |
| [31] | Fullerton, R. L.; McAfee, R. P., Auctioning entry into tournaments, J. Polit. Econ., 107, 573-605 (1999) |
| [32] | Gerchak, Y.; He, Q.-M., When will the range of prizes in tournaments increase in the noise or in the number of players?, Int. Game Theory Rev., 05, 151-165 (2003) · Zbl 1135.91004 |
| [33] | Ghosh, S.; Waldman, M., Standard promotion practices versus up-or-out contracts, Rand J. Econ., 41, 301-325 (2010) |
| [34] | Gilpatric, S. M., Risk taking in contests and the role of carrots and sticks, Econ. Inq., 47, 266-277 (2009) |
| [35] | Green, J. R.; Stokey, N. L., A comparison of tournaments and contracts, J. Polit. Econ., 91, 349-364 (1983) |
| [36] | Grund, C.; Sliwka, D., Envy and compassion in tournaments, J. Econ. Manag. Strategy, 14, 187-207 (2005) |
| [37] | Gürtler, M.; Gürtler, O., The optimality of heterogeneous tournaments, J. Labor Econ., 33, 1007-1042 (2015) |
| [38] | Gürtler, M.; Gürtler, O., Promotion signaling, discrimination, and positive discrimination policies, Rand J. Econ., 50, 1004-1027 (2019) |
| [39] | Hillman, A. L.; Riley, J. G., Politically contestable rents and transfers, Econ. Polit., 1, 17-39 (1989) |
| [40] | Holmström, B., Managerial incentive problems: a dynamic perspective, (Essays in Economics and Management in Honor of Lars Wahlbeck. Essays in Economics and Management in Honor of Lars Wahlbeck, Helsinki, 1982 (1982)). (Essays in Economics and Management in Honor of Lars Wahlbeck. Essays in Economics and Management in Honor of Lars Wahlbeck, Helsinki, 1982 (1982)), Rev. Econ. Stud., 66, 1, 169-182 (1999), Reprinted in: · Zbl 0948.91042 |
| [41] | Holmström, B.; Ricard I. Costa, J., Managerial incentives and capital management, Q. J. Econ., 101, 835-860 (1986) |
| [42] | Hvide, H. K., Tournament rewards and risk taking, J. Labor Econ., 20, 877-898 (2002) |
| [43] | Imhof, L.; Kräkel, M., Ex post unbalanced tournaments, Rand J. Econ., 47, 73-98 (2016) |
| [44] | Jia, H., A stochastic derivation of the ratio form of contest success functions, Public Choice, 135, 125-130 (2008) |
| [45] | Kirkegaard, R., Contest design with stochastic performance, Am. Econ. J. Microecon. (2022), Forthcoming |
| [46] | Konrad, K. A., Strategy and Dynamics in Contests (2009), Oxford University Press · Zbl 1182.91004 |
| [47] | Kräkel, M., Optimal risk taking in an uneven tournament game with risk averse players, J. Math. Econ., 44, 1219-1231 (2008) · Zbl 1148.91006 |
| [48] | Kräkel, M.; Sliwka, D., Risk taking in asymmetric tournaments, Ger. Econ. Rev., 5, 103-116 (2004) |
| [49] | Krumer, A.; Megidish, R.; Sela, A., Round-robin tournaments with a dominant player, Scand. J. Econ., 119, 1167-1200 (2017) · Zbl 1397.91266 |
| [50] | Lazear, E. P., Pay equality and industrial politics, J. Polit. Econ., 97, 561-580 (1989) |
| [51] | Lazear, E. P.; Rosen, S., Rank-order tournaments as optimum labor contracts, J. Polit. Econ., 89, 841-864 (1981) |
| [52] | Levy, H., Stochastic dominance and expected utility: survey and analysis, Manag. Sci., 38, 555-593 (1992) · Zbl 0764.90004 |
| [53] | Lu, J.; Wang, Z.; Zhou, L., Optimal favoritism in contests with identity-contingent prizes (2021), Working Paper |
| [54] | Malcomson, J. M., Work incentives, hierarchy, and internal labor markets, J. Polit. Econ., 92, 486-507 (1984) |
| [55] | Malcomson, J. M., Rank-order contracts for a principal with many agents, Rev. Econ. Stud., 53, 807-817 (1986) · Zbl 0604.90040 |
| [56] | Moldovanu, B.; Sela, A., The optimal allocation of prizes in contests, Am. Econ. Rev., 91, 542-558 (2001) |
| [57] | Moldovanu, B.; Sela, A., Contest architecture, J. Econ. Theory, 126, 70-96 (2006) · Zbl 1108.91008 |
| [58] | Moldovanu, B.; Sela, A.; Shi, X., Contests for status, J. Polit. Econ., 115, 338-363 (2007) |
| [59] | Morath, F.; Münster, J., Information acquisition in conflicts, Econ. Theory, 54, 99-129 (2013) · Zbl 1295.91052 |
| [60] | Münster, J., Group contest success functions, Econ. Theory, 41, 345-357 (2009) · Zbl 1180.91069 |
| [61] | Nalebuff, B. J.; Stiglitz, J. E., Prizes and incentives: towards a general theory of compensation and competition, Bell J. Econ., 14, 21-43 (1983) |
| [62] | O’Keeffe, M.; Viscusi, W. K.; Zeckhauser, R. J., Economic contests: comparative reward schemes, J. Labor Econ., 2, 27-56 (1984) |
| [63] | Olszewski, W.; Siegel, R., Large contests, Econometrica, 84, 835-854 (2016) · Zbl 1419.91339 |
| [64] | Owan, H., Promotion, turnover, earnings, and firm-sponsored training, J. Labor Econ., 22, 955-978 (2004) |
| [65] | Pérez-Castrillo, D.; Wettstein, D., Discrimination in a model of contests with incomplete information about ability, Int. Econ. Rev., 57, 881-914 (2016) · Zbl 1404.91131 |
| [66] | Rinne, H., The hazard rate: theory and inference - with supplementary MATLAB programs (2014), Justus-Liebig-University: Justus-Liebig-University Giessen, Germany, Technical Report |
| [67] | Rothschild, M.; Stiglitz, J. E., Increasing risk I: a definition, J. Econ. Theory, 2, 225-243 (1970) |
| [68] | Ryvkin, D.; Drugov, M., The shape of luck and competition in winner-take-all tournaments, Theor. Econ., 15, 1587-1626 (2020) · Zbl 1466.91009 |
| [69] | Schotter, A.; Weigelt, K., Asymmetric tournaments, equal opportunity laws, and affirmative action: some experimental results, Q. J. Econ., 107, 511-539 (1992) |
| [70] | Schöttner, A.; Thiele, V., Promotion tournaments and individual performance pay, J. Econ. Manag. Strategy, 19, 699-731 (2010) |
| [71] | Schweinzer, P.; Segev, E., The optimal prize structure of symmetric Tullock contests, Public Choice, 153, 69-82 (2012) |
| [72] | Sela, A., Sequential two-prize contests, Econ. Theory, 51, 383-395 (2012) · Zbl 1262.91089 |
| [73] | Siegel, R., All-pay contests, Econometrica, 77, 71-92 (2009) · Zbl 1160.91315 |
| [74] | Siegel, R., Asymmetric contests with conditional investments, Am. Econ. Rev., 100, 2230-2260 (2010) |
| [75] | Skaperdas, S., Contest success functions, Econ. Theory, 7, 283-290 (1996) · Zbl 0852.90137 |
| [76] | Tullock, G., Efficient rent seeking, (Buchanan, J.; Tollison, R.; Tullock, G., Towards a Theory of the Rent-Seeking Society (1980), Texas A&M University Press: Texas A&M University Press College Station, TX), 97-112 |
| [77] | Vojnović, M., Contest Theory: Incentive Mechanisms and Ranking Methods (2016), Cambridge University Press |
| [78] | Waldman, M., Job assignments, signalling, and efficiency, Rand J. Econ., 15, 255-267 (1984) |
| [79] | Zábojník, J., Promotion tournaments in market equilibrium, Econ. Theory, 51, 213-240 (2012) · Zbl 1247.91098 |
| [80] | Zábojník, J.; Bernhardt, D., Corporate tournaments, human capital acquisition, and the firm size—wage relation, Rev. Econ. Stud., 68, 693-716 (2001) · Zbl 0999.91053 |
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