Winner-Take-All and Proportional-Prize Contests: Theory and Experimental Results

Cason, Timothy and Masters, William and Sheremeta, Roman (2018): Winner-Take-All and Proportional-Prize Contests: Theory and Experimental Results. Forthcoming in: Journal of Economic Behavior and Organization

Abstract

This study provides a unified framework to compare three canonical types of contests: winner-take-all contests won by the best performer, winner-take-all lotteries where probability of success is proportional to performance, and proportional-prize contests in which rewards are shared in proportion to performance. We derive equilibria and observe outcomes from each contest in a laboratory experiment. Equilibrium and observed efforts are highest in winner-take-all contests. Lotteries and proportional-prize contests have the same Nash equilibrium, but empirically, lotteries induce higher efforts and lower, more unequal payoffs. Behavioral deviations from theoretical benchmarks in different contests are caused by the same underlying attributes, such as risk-aversion and the utility of winning. Finally, we find that subjects exhibit consistent behavior across different types of contests, with subjects exerting higher effort in one contest also exerting higher effort in another contest.

• Item Type: MPRA Paper
• Language: English
• Keywords: contests, rent-seeking, lotteries, incentives in experiments, risk aversion
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D74 - Conflict ; Conflict Resolution ; Alliances ; Revolutions; J - Labor and Demographic Economics > J3 - Wages, Compensation, and Labor Costs > J33 - Compensation Packages ; Payment Methods

References

Agranov, M., & Tergiman, C. (2013). Incentives and compensation schemes: An experimental study. International Journal of Industrial Organization, 31, 238-247.

Amegashie, J. (2006). A contest success function with a tractable noise parameter. Public Choice, 126, 135-144.

Balafoutas, L., Kerschbamer, R. & Sutter, M. (2012). Distributional preferences and competitive behavior. Journal of Economic Behavior and Organization, 83, 125-135.

Bartling, B., Fehr, E., Marechal, M.A., & Schunk, D. (2009). Egalitarianism and Competitiveness. American Economic Review, 99, 93-98.

Baye, M.R., Hoppe, H.C. (2003). The strategic equivalence of rent-seeking, innovation, and patent-race games. Games and Economic Behavior, 44, 217-226.

Baye, M.R., Kovenock, D. & de Vries, C.G. (1996). The all-pay auction with complete information. Economic Theory, 8, 291-305.

Brown, J. (2011). Quitters never win: The (adverse) incentive effects of competing with superstars. Journal of Political Economy, 119, 982-1013.

Bull, C., Schotter, A. & Weigelt, K., (1987). Tournaments and piece rates: an experimental study. Journal of Political Economy 95, 1-33.

Cason, T.N., Masters, W.A. & Sheremeta, R.M. (2010). Entry into winner-take-all and proportional-prize contests: An experimental study. Journal of Public Economics, 94, 604-611.

Cason, T.N., Sheremeta, R.M., & Zhang, J. (2017). Asymmetric and endogenous within-group communication in competitive coordination games. Experimental Economics, 20, 946-972.

Cason, T.N., Sheremeta, R.M., & Zhang, J. (2012). Communication and efficiency in competitive coordination games. Games and Economic Behavior, 76, 26-43.

Che, Y.K., & Gale, I. (2000). Difference-form contests and the robustness of all-pay auctions, Games and Economic Behavior, 30, 22-43.

Chowdhury, S.M., & Sheremeta, R.M. (2015). Strategically equivalent contests. Theory and Decision, 78, 587-601.

Chowdhury, S. M., Sheremeta, R. M., & Turocy, T. L. (2014). Overbidding and overspreading in rent-seeking experiments: Cost structure and prize allocation rules. Games and Economic Behavior, 87, 224-238.

Dasgupta, A., & Nti, K.O. (1998). Designing an optimal contest. European Journal of Political Economy, 14, 587-603.

Davis, D. & Reilly, R. (1998). Do many cooks always spoil the stew? An experimental analysis of rent seeking and the role of a strategic buyer. Public Choice, 95, 89-115.

Dechenaux, E., Kovenock, D., & Sheremeta, R.M. (2015). A survey of experimental research on contests, all-pay auctions and tournaments. Experimental Economics, 18, 609-669.

Delgado, M., Schotter, A., Ozbay, E. & Phelps, E. (2008). Understanding overbidding: Using the neural circuitry of reward to design economic auctions. Science, 321, 1849-1852.

Eisenkopf, G. & Teyssier, S. (2013). Envy and loss aversion in tournaments. Journal of Economic Psychology, 34, 240-255.

Eriksson, T., Teyssier, S. & Villeval, M.C. (2009). Self-selection and the efficiency of tournaments. Economic Inquiry, 47, 530-548.

Fallucchi, F., Renner, E. & Sefton, M. (2013). Information feedback and contest structure in rent-seeking games. European Economic Review, 64, 223-240.

Fang, H. (2002). Lottery versus all-pay auction models of lobbying. Public Choice, 112, 351-371.

Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic Experiments. Experimental Economics, 10, 171-178.

Fonseca, M.A. (2009). An experimental investigation of asymmetric contests. International Journal of Industrial Organization, 27, 582-591.

Frank, R.H. and Cook, P. (1995). The winner-take-all society. Penguin Books, New York, New York.

Fu, Q., & Lu, J. (2012). Micro foundations of multi-prize lottery contests: a perspective of noisy performance ranking. Social Choice and Welfare, 38, 497-517.

Fudenberg, D., Gilbert, R., Stiglitz, J., & Tirole, J. (1983). Preemption, leapfrogging and competition in patent races. European Economic Review, 22, 3-31.

Gerchak, Y. & He, Q.M. (2003). When will the range of prizes in tournaments increase in the noise or in the number of players? International Game Theory Review, 5, 151-166.

Gill, D. & Stone, R. (2010). Fairness and desert in tournaments. Games and Economic Behavior, 69, 346-364.

Gradstein, M. (1998). Optimal contest design: volume and timing of rent seeking in contests. European Journal of Political Economy, 14, 575-585.

Grund, C., & Sliwka, D. (2005). Envy and compassion in tournaments. Journal of Economics and Management Strategy, 14, 187-207.

Harbring, C. & Irlenbusch, B. (2003). An experimental study on tournament design. Labour Economics, 10, 443-464.

Harris, C., & Vickers, J. (1985). Perfect equilibrium in a model of a race. Review of Economic Studies, 52, 193-209.

Harris, C., & Vickers, J. (1987). Racing with uncertainty. Review of Economic Studies, 54, 1-21.

Herrmann, B., & Orzen, H. (2008). The appearance of homo rivalis: social preferences and the nature of rent seeking. University of Nottingham, Working Paper.

Hillman, A. & Riley, J.G., (1989). Politically contestable rents and transfers. Economics and Politics, 1, 17-40.

Hirshleifer, J. & Riley, J.G. (1992). The analytics of uncertainty and information. New York: Cambridge University Press.

Holmström, B. (1979). Moral hazard and observability. Bell Journal of Economics, 10, 74-91.

Holt, C.A. & Laury, S.K. (2002). Risk aversion and incentive effects. American Economic Review, 92, 1644-1655.

Jia, H. (2008). A stochastic derivation of the ratio form of contest success functions. Public Choice, 135, 125-130.

Kimbrough, E.O, Laughren, K., & Sheremeta, R.M. (2018). War and conflict in economics: Theories, applications, and recent trends. Journal of Economic Behavior and Organization, forthcoming.

Kimbrough, E.O., Sheremeta, R.M., & Shields, T.W. (2014). When parity promotes peace: Resolving conflict between asymmetric agents. Journal of Economic Behavior and Organization, 99, 96-108.

Konrad, K.A. (2009). Strategy and dynamics in contests. New York, NY: Oxford University Press.

Krueger, A.O. (1974). The political economy of the rent-seeking society. American Economic Review, 64, 291-303.

Lazear, E.P., & Rosen, S. (1981). Rank-order tournaments as optimum labor contracts. Journal of Political Economy, 89, 841-864.

Llorente-Saguer, A., Sheremeta, R.M., & Szech, N. (2016). How to design contests between heterogeneous contestants: An experimental study of tie-breaks and bid-caps in all-pay auctions. Working Paper.

Long, N.V., & Vousden, N. (1987). Risk-averse rent seeking with shared rents. Economic Journal, 97, 971-985.

Mago, S.D., & Sheremeta, R.M. (2018). Multi-battle contests: An experimental study. Southern Economic Journal, forthcoming.

Mago, S.D., Samek, A., & Sheremeta, R.M. (2016). Facing your opponents: Social Identification and Information Feedback in Contests. Journal of Conflict Resolution, 60, 459-481.

Mago, S.D., Sheremeta, R.M., & Yates, A. (2013). Best-of-three contest experiments: Strategic versus psychological momentum. International Journal of Industrial Organization, 31, 287-296.

Masiliunas, A., Mengel, F., & Reiss, J.P. (2014). Behavioral variation in Tullock contests. Working Paper.

McKinsey & Company (2009). ‘And the winner is…’: Capturing the promise of philanthropc prizes. Online at http://mckinseyonsociety.com/capturing-the-promise-of-philanthropic-prizes.

Millner, E.L., & Pratt, M.D. (1989). An experimental investigation of efficient rent-seeking. Public Choice, 62, 139-151.

Millner, E.L., & Pratt, M.D. (1991). Risk aversion and rent-seeking: An extension and some experimental evidence. Public Choice, 69, 81-92.

Moldovanu, B., & Sela, A. (2001). The optimal allocation of prizes in contests. American Economic Review, 542-558.

Morgan, J., & Sefton, M. (2000). Funding public goods with lotteries: Experimental Evidence. Review of Economic Studies, 67, 785-810.

Morgan, J., Orzen, H., Sefton, M., & Sisak, D. (2016). Strategic and natural risk in entrepreneurship: An experimental study. Journal of Economics & Management Strategy, 25, 420-454.

O'Keeffe, M.W., Viscusi, K. & Zeckhauser, I.L., (1984). Economic contests: Comparative reward schemes. Journal of Labor Economics, 2, 27-56.

Potters, J.C., De Vries, C.G., & Van Linden, F. (1998). An experimental examination of rational rent seeking. European Journal of Political Economy, 14, 783-800.

Price, C.R., & Sheremeta, R.M. (2011). Endowment effects in contests. Economics Letters, 111, 217-219.

Price, C.R., & Sheremeta, R.M. (2015). Endowment origin, demographic effects and individual preferences in contests. Journal of Economics and Management Strategy, 24, 597-619.

Rosen, S. (1986). Prizes and incentives in elimination tournaments. American Economic Review, 76, 701-715.

Rubin, J., & Sheremeta, R. (2015). Principal–agent settings with random shocks. Management Science, 62, 985-999.

Schotter, A., & Weigelt, K. (1992). Asymmetric tournaments, equal opportunity laws, and affirmative action: Some experimental results. Quarterly Journal of Economics, 107, 511-539.

Sheremeta, R.M. (2010). Experimental comparison of multi-stage and one-stage contests. Games and Economic Behavior, 68, 731-747.

Sheremeta, R.M. (2011). Contest design: An experimental investigation. Economic Inquiry, 49, 573-590.

Sheremeta, R.M. (2013). Overbidding and heterogeneous behavior in contest experiments. Journal of Economic Surveys, 27, 491-514.

Sheremeta, R.M. (2015). Behavioral dimensions of contests. In Congleton, R.D., Hillman, A.L., (Eds.), Companion to political economy of rent seeking, London: Edward Elgar, pp. 150-164.

Sheremeta, R.M. (2016). Impulsive behavior in competition: Testing theories of overbidding in rent-seeking contests. Working Paper.

Shupp, R., Sheremeta, R.M., Schmidt, D., & Walker, J. (2013). Resource allocation contests: Experimental evidence. Journal of Economic Psychology, 39, 257-267.

Singh, P., & Masters, W.A. (2017a). Impact of caregiver incentives on child health: Evidence from an experiment with Anganwadi workers in India. Journal of Health Economics, 55, 219-231.

Singh, P., & Masters, W.A. (2017b). Performance bonuses in the public sector: Winner-take-all prizes versus proportional payments to reduce child malnutrition in India. Working paper.

Skaperdas, S. (1996). Contest success functions. Economic Theory, 7, 283-290.

Snyder, J. (1989). Election goals and the allocation of campaign resources. Econometrica, 57, 630-660.

Tullock, G. (1980). Efficient rent seeking. In James M. Buchanan, Robert D. Tollison, Gordon Tullock, (Eds.), Toward a theory of the rent-seeking society. College Station, TX: Texas A&M University Press, pp. 97-112.

Weigelt, K., Dukerich, J., & Schotter, A. (1989). Reactions to discrimination in an incentive pay compensation scheme: A game-theoretic approach. Organizational Behavior and Human Decision Processes, 44, 26-44.

Weitzman M.L., & Kruse, D.L. (1990). Profit sharing and productivity, in A. Blinder (ed.) Paying for Productivity, Brookings.

Zheng, X., & Vukina, T. (2007). Efficiency gains from organizational innovation: Comparing ordinal and cardinal tournament games in broiler contracts. International Journal of Industrial Organization, 25, 843-859.