Grading in Games of Status: Marking Exams and Setting Wages
We introduce grading into games of status. Each player chooses effort, producing a stochastic output or score. Utilities depend on the ranking of all the scores. By clustering scores into grades, the ranking is coarsened, and the incentives to work are changed. We first apply games of status to grading exams. Our main conclusion is that if students care primarily about their status (relative rank) in class, they are often best motivated to work not by revealing their exact numerical exam scores (100,99,...,1), but instead by clumping them into coarse categories (A,B,C). When student abilities are disparate, the optimal grading scheme is always coarse. Furthermore, it awards fewer A's than there are alpha-quality students, creating small elites. When students are homogeneous, we characterize optimal grading schemes in terms of the stochastic dominance between student performances (when they shirk or work) on subintervals of scores, showing again why coarse grading may be advantageous. In both the disparate case and the homogeneous case, we prove that absolute grading is better than grading on a curve, provided student scores are independent. We next bring games of money and status to bear on the optimal wage schedule: workers can be motivated not merely by the purchasing power of wages, but also by the status higher wages confer. How should the employer combine both incentive devices to generate an optimal pay schedule? When workers' abilities are disparate, the optimal wage schedule creates different grades than we found with status incentives alone. The very top type should be motivated solely by money, with enormous salaries going to a tiny elite. Furthermore, if the population of workers diminishes as we go up the ability ladder and their disutility for work does not fall as fast, then the optimal wage schedule exhibits increasing wage differentials, despite the linearity in production. When workers are homogeneous, the same status grades are optimal as we found with status incentives alone. A bonus is paid only to scores in the top status grade.
|Date of creation:||Dec 2005|
|Date of revision:||Dec 2005|
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- Harold L. Cole & George J. Mailath & Andrew Postlewaite, 1996.
"Class systems and the enforcement of social norms,"
213, Federal Reserve Bank of Minneapolis.
- Harold L. Cole & George J. Mailath & Andrew Postlewaite, . "Class Systems and the Enforcement of Social Norms," CARESS Working Papres 97-3, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- Harold L. Cole & George J. Mailath & Andrew Postlewaite, . ""Class Systems and the Enforcement of Social Norms''," CARESS Working Papres 96-04, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- Harold L. Cole & George J. Mailath & Andrew Postlewaite, . "Class Systems and the Enforcement of Social Norms," Penn CARESS Working Papers bdb2c3969ad56e98068513c7c, Penn Economics Department.
- Fehr, Ernst & Schmidt, Klaus M., 1998.
"A Theory of Fairness, Competition and Cooperation,"
CEPR Discussion Papers
1812, C.E.P.R. Discussion Papers.
- Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 817-868.
- Fehr, Ernst & Schmidt, Klaus M., . "A theory of fairness, competition, and cooperation," Chapters in Economics, University of Munich, Department of Economics.
- Ernst Fehr & Klaus M. Schmidt, . "A Theory of Fairness, Competition and Cooperation," IEW - Working Papers 004, Institute for Empirical Research in Economics - University of Zurich.
- Fehr, Ernst & Schmidt, Klaus M., 1999. "A theory of fairness, competition, and cooperation," Munich Reprints in Economics 20650, University of Munich, Department of Economics.
- Dubey, Pradeep & Haimanko, Ori, 2003.
"Optimal scrutiny in multi-period promotion tournaments,"
Games and Economic Behavior,
Elsevier, vol. 42(1), pages 1-24, January.
- Pradeep Dubey & Ori Haimanko, 2000. "Optimal Scrutiny in Multi-Period Promotion Tournaments," Cowles Foundation Discussion Papers 1254, Cowles Foundation for Research in Economics, Yale University.
- Lazear, Edward P & Rosen, Sherwin, 1981.
"Rank-Order Tournaments as Optimum Labor Contracts,"
Journal of Political Economy,
University of Chicago Press, vol. 89(5), pages 841-64, October.
- repec:adr:anecst:y:2001:i:63-64 is not listed on IDEAS
- Moldovanu, Benny & Sela, Aner, 1999.
"The Optimal Allocation of Prizes in Contests,"
Sonderforschungsbereich 504 Publications
99-75, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
- Pradeep Dubey & John Geanakoplos, 2004. "Grading Exams: 100, 99, ..., 1 or A, B, C? Incentives in Games of Status," Cowles Foundation Discussion Papers 1467, Cowles Foundation for Research in Economics, Yale University.
- Pollak, Robert A, 1976. "Interdependent Preferences," American Economic Review, American Economic Association, vol. 66(3), pages 309-20, June.
- Cole, Harold L & Mailath, George J & Postlewaite, Andrew, 1992. "Social Norms, Savings Behavior, and Growth," Journal of Political Economy, University of Chicago Press, vol. 100(6), pages 1092-1125, December.
- Green, Jerry R & Stokey, Nancy L, 1983.
"A Comparison of Tournaments and Contracts,"
Journal of Political Economy,
University of Chicago Press, vol. 91(3), pages 349-64, June.
- Green, Jerry & Stokey, Nancy, 1983. "A Comparison of Tournaments and Contracts," Scholarly Articles 3203644, Harvard University Department of Economics.
- Jerry R. Green & Nancy L. Stokey, 1982. "A Comparison of Tournaments and Contracts," NBER Working Papers 0840, National Bureau of Economic Research, Inc.
- Corneo, Giacomo & Jeanne, Olivier, 1997. "On relative wealth effects and the optimality of growth," Economics Letters, Elsevier, vol. 54(1), pages 87-92, January.
- Robson, Arthur J, 1992. "Status, the Distribution of Wealth, Private and Social Attitudes to Risk," Econometrica, Econometric Society, vol. 60(4), pages 837-57, July.
- Alexis Direr, 2001. "Interdependent Preferences and Aggregate Saving," Annals of Economics and Statistics, GENES, issue 63-64, pages 297-308.
- repec:adr:anecst:y:2001:i:63-64:p:15 is not listed on IDEAS
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