Fairness and Desert in Tournaments

Gill, David and Stone, Rebecca (2010): Fairness and Desert in Tournaments. Forthcoming in: Games and Economic Behavior

Abstract

We model the behavior of agents who care about receiving what they feel they deserve in a two-player rank-order tournament. Perceived entitlements are sensitive to how hard an agent has worked relative to her rival, and agents are loss averse around their meritocratically determined endogenous reference points. In a fair tournament sufficiently large desert concerns drive identical agents to push their effort levels apart in order to end up closer to their reference points on average. In an unfair tournament, where one agent is advantaged, the equilibrium is symmetric in the absence of desert, but asymmetric in the presence of desert. We find that desert concerns can undermine the standard conclusion that competition for a fixed supply of status is socially wasteful and explain why, when the distribution of output noise is fat-tailed, an employer might use a rank-order incentive scheme.

• Item Type: MPRA Paper
• Language: English
• Keywords: Desert, Equity, Tournament, Loss Aversion, Reference-Dependent Preferences, Reference Point, Psychological Game Theory, Status, Relative Performance Evaluation
• Subjects: D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement; J - Labor and Demographic Economics > J3 - Wages, Compensation, and Labor Costs > J33 - Compensation Packages ; Payment Methods

References

Adams, J.S., 1965. Inequity in social exchange. In: Berkowitz, L. (Ed.), Advances in Experimental Social Psychology, Vol. II. Academic Press, New York, pp. 267-299.

Barberis, N., Huang, M., Thaler, R.H., 2006. Individual preferences, monetary gambles, and stock market participation: A case for narrow framing. Amer. Econ. Rev. 96, 1069-1090.

Bartling, B., von Siemens, F., 2004. Efficiency in team production with inequity averse agents. Mimeo, University of Munich.

Battigalli, P., Dufwenberg, M., 2007. Guilt in games. Amer. Econ. Rev. Papers and Proceedings 97, 170-176.

Battigalli, P., Dufwenberg, M., 2009. Dynamic psychological games. J. Econ. Theory, 144, 1-35.

Bell, D.E., 1985. Disappointment in decision making under uncertainty. Operations Research 33, 1-27.

Bolton, G.E., Ockenfels, A., 2000. ERC: A theory of equity, reciprocity and competition. Amer. Econ. Rev. 90, 166-193.

Bull, C., Schotter, A., Weigelt, K., 1987. Tournaments and piece rates: An experimental study. J. Polit. Economy 95, 1-33.

Burrows, P., Loomes, G., 1994. The impact of fairness on bargaining behaviour. Empirical Econ. 19, 201-221.

Cappelen, A.W., Hole, A.D., Sørensen, E.O., Tungodden, B., 2007. The pluralism of fairness ideals: An experimental approach. Amer. Econ. Rev. 97, 818-827.

Chowdhury, S.M., Sheremeta, R.M., 2009. A generalized Tullock contest and the existence of multiple equilibria. Mimeo, University of East Anglia.

Conyon, M.J., Peck, S.I., Sadler, G.V., 2001. Corporate tournaments and executive compensation: Evidence from the U.K. Strategic Management Journal 22, 805-815.

Cornes, R., Hartley, R., 2003. Loss aversion and the Tullock paradox. Keele Economics Research Papers 2003/06.

Demougin, D., Fluet, C., 2003. Inequity aversion in tournaments. CIRPEE Working Paper No. 03-22. D eVaro, J., 2006. Internal promotion competitions in firms. RAND J. Econ. 37, 521-542.

van Dijk, F., Sonnemans, J., van Winden, F., 2001. Incentive systems in a real effort experiment. Europ. Econ. Rev. 45, 187-214.

Dufwenberg, M., Kirchsteiger, G., 2004. A theory of sequential reciprocity. Games Econ. Behav. 47, 268-298.

Ederer, F., Fehr, E., 2006. Communication and information in dynamic tournaments: Theory and evidence. Mimeo, MIT.

Englmaier, F., 2005. A survey on moral hazard, contracts, and social preferences. In: Agarwal, B., Vercelli, A. (Eds.), Psychology, Rationality and Economic Behaviour: Challenging Standard Assumptions. Palgrave Macmillan, pp. 125-140.

Falk, A., Fischbacher, U., 2006. A theory of reciprocity. Games Econ. Behav. 54, 293-315.

Fehr, E., Schmidt, K., 1999. A theory of fairness, competition and cooperation. Quart. J. Econ. 114, 817-868.

Frank, R.H., 2005. Positional externalities cause large and preventable welfare losses. Amer. Econ. Rev. Papers and Proceedings 95, 137-141.

Frohlich, N., Oppenheimer, J., Kurki, A., 2004. Modeling other-regarding preferences and an experimental test. Public Choice 119, 91-117.

Fudenberg, D., Tirole, J., 1991. Game Theory. MIT Press, Cambridge, Mass.

Geanakoplos, J., Pearce D., Stacchetti, E., 1989. Psychological games and sequential rationality. Games Econ. Behav. 1, 60-79.

Gill, D., Prowse, V., 2009. A structural analysis of disappointment aversion in a real effort competition. IZA Discussion Paper 4536.

Gill, D., Stone, R., 2006. Fairness and desert in tournaments. Department of Economics Discussion Paper 279, University of Oxford.

Gneezy, U., List, J.A., Wu, G., 2006. The uncertainty effect: When a risky prospect is valued less than its worst possible outcome. Quart. J. Econ. 121, 1283-1309.

Green, J.R., Stokey, N.L., 1983. A comparison of tournaments and contracts. J. Polit. Economy 91, 349-364.

Grund, C., Sliwka, D., 2005. Envy and compassion in tournaments. J. Econ. Manage. Strategy 14, 187-207.

Güth, W., 1988. On the behavioral approach to distributive justice - A theoretical and experimental investigation. In: Maital, S. (Ed.), Applied Behavioural Economics, Vol. II. Wheatsheaf, Brighton, pp. 703-717.

Harbring, C., Irlenbusch, B., 2003. An experimental study on tournament design. Lab. Econ. 10, 443-464.

Hopkins, E., Kornienko, T., 2004. Running to keep in the same place: Consumer choice as a game of status. Amer. Econ. Rev. 94, 1085-1107.

Itoh, H., 2004. Moral hazard and other-regarding preferences. Japanese Econ. Rev. 55, 18-45.

Kahneman, D., Knetsch, J.L., Thaler, R., 1986. Fairness as a constraint on profit seeking: Entitlements in markets. Amer. Econ. Rev. 76, 728-741.

Kahneman, D., Tversky, A., 1979. Prospect theory: An analysis of decision under risk. Econometrica 47, 263-291.

Konow, J., 1996. A positive theory of economic fairness. J. Econ. Behav. Organ. 31, 13-35.

Konow, J., 2000. Fair shares: Accountability and cognitive dissonance in allocation decisions. Amer. Econ. Rev. 90, 1072-1091.

Konow, J., 2003. Which is the fairest one of all? A positive analysis of justice theories. J. Econ. Lit. 41, 1188-1239.

Kőszegi, B., Rabin, M., 2006. A model of reference-dependent preferences. Quart. J. Econ. 121, 1133-1165.

Kőszegi, B., Rabin, M., 2007. Reference-dependent risk attitudes. Amer. Econ. Rev. 97, 1047-1073.

Lazear, E.P., Rosen, S., 1981. Rank-order tournaments as optimal labor contracts. J. Polit. Economy 89, 841-864.

Loomes, G., Sugden, R., 1986. Disappointment and dynamic consistency in choice under uncertainty. Rev. Econ. Stud. 53, 271-282.

Malcomson, J.M., 1984. Work incentives, hierarchy, and internal labor markets. J. Polit. Economy 92, 486-507.

McLaughlin, K.J., 1988. Aspects of tournament models: A survey. In: Ehrenberg, R. (Ed.), Research in Labor Economics, Vol. 9. JAI Press, Greenwich, pp. 225-256.

Mellers, B., Schwartz A., Ritov, I., 1999. Emotion-based choice. Journal of Experimental Psychology: General 128, 332-345.

Nalebuff, B.J., Stiglitz, J.E., 1983. Prizes and incentives: Towards a general theory of compensation and competition. Bell J. Econ. 14, 21-43.

Prendergast, C., 1999. The provision of incentives in firms. J. Econ. Lit. 37, 7-63.

Rabin, M., 1993. Incorporating fairness into game theory and economics. Amer. Econ. Rev. 83, 1281-1302.

Rabin, M., 1998. Psychology and economics. J. Econ. Lit. 36, 11-46.

Rey Biel, P., 2008. Inequity aversion and team incentives. Scand. J. Econ. 110, 297-320.

Schotter, A., Weigelt, K., 1992. Asymmetric tournaments, equal opportunity laws, and affirmative action: Some experimental results. Quart. J. Econ. 107, 511-539.

Sheremeta, R.M., 2009. Experimental comparison of multi-stage and one-stage contests. Games Econ. Behav. forthcoming. (doi:10.1016/j.geb.2009.08.001)

Stone, R., 2004. Self-handicapping, tournaments and ego utility. Mimeo, UCL.