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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d15a/d1544.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1544.

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Length: 48 pages
Date of creation: Dec 2005
Date of revision:
Handle: RePEc:cwl:cwldpp:1544
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Web page: http://cowles.econ.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Green, Jerry & Stokey, Nancy, 1983. "A Comparison of Tournaments and Contracts," Scholarly Articles 3203644, Harvard University Department of Economics.
  2. Moldovanu, Benny & Sela, Aner, 1999. "The Optimal Allocation of Prizes in Contests," Sonderforschungsbereich 504 Publications 99-75, Sonderforschungsbereich 504, Universit├Ąt Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  3. Pollak, Robert A, 1976. "Interdependent Preferences," American Economic Review, American Economic Association, vol. 66(3), pages 309-20, June.
  4. Cole, Harold L. & Mailath, George J. & Postlewaite, Andrew, 1998. "Class systems and the enforcement of social norms," Journal of Public Economics, Elsevier, vol. 70(1), pages 5-35, October.
  5. Fehr, Ernst & Schmidt, Klaus M., 1998. "A Theory of Fairness, Competition and Cooperation," CEPR Discussion Papers 1812, C.E.P.R. Discussion Papers.
  6. 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.
  7. 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.
  8. Dubey, Pradeep & Haimanko, Ori, 2003. "Optimal scrutiny in multi-period promotion tournaments," Games and Economic Behavior, Elsevier, vol. 42(1), pages 1-24, January.
  9. 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.
  10. Corneo, Giacomo & Jeanne, Olivier, 1997. "On relative wealth effects and the optimality of growth," Economics Letters, Elsevier, vol. 54(1), pages 87-92, January.
  11. 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.
  12. Alexis DIRER, 2001. "Interdependent Preferences and Aggregate Saving," Annales d'Economie et de Statistique, ENSAE, issue 63-64, pages 297-308.
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