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Grading in Games of Status: Marking Exams and Setting Wages

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    Abstract

    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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    Bibliographic Info

    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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    Fax: (203) 432-6167
    Web page: http://cowles.econ.yale.edu/
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    Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

    Related research

    Keywords: Status; Grading; Incentives; Education; Exams; Wages;

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    References

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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. 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.
    3. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
    4. Dubey, Pradeep & Haimanko, Ori, 2003. "Optimal scrutiny in multi-period promotion tournaments," Games and Economic Behavior, Elsevier, vol. 42(1), pages 1-24, January.
    5. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory Of Fairness, Competition, And Cooperation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 817-868, August.
    6. Alexis DIRER, 2001. "Interdependent Preferences and Aggregate Saving," Annales d'Economie et de Statistique, ENSAE, issue 63-64, pages 297-308.
    7. Pollak, Robert A, 1976. "Interdependent Preferences," American Economic Review, American Economic Association, vol. 66(3), pages 309-20, June.
    8. 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.
    9. Corneo, Giacomo & Jeanne, Olivier, 1997. "On relative wealth effects and the optimality of growth," Economics Letters, Elsevier, vol. 54(1), pages 87-92, January.
    10. Edward P. Lazear & Sherwin Rosen, 1979. "Rank-Order Tournaments as Optimum Labor Contracts," NBER Working Papers 0401, National Bureau of Economic Research, Inc.
    11. 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.
    12. Jerry R. Green & Nancy L. Stokey, 1982. "A Comparison of Tournaments and Contracts," NBER Working Papers 0840, National Bureau of Economic Research, Inc.
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    Cited by:
    1. Ramalingam, Abhijit, 2009. ""Endogenous" Relative Concerns: The Impact of Workers' Characteristics on Status and Pro ts in the Firm," MPRA Paper 18759, University Library of Munich, Germany.
    2. Hopkins, Ed & Kornienko, Tatiana, 2009. "Status, affluence, and inequality: Rank-based comparisons in games of status," Games and Economic Behavior, Elsevier, vol. 67(2), pages 552-568, November.
    3. Pradeep Dubey & Siddhartha Sahi, 2009. "The Allocation of a Prize," Department of Economics Working Papers 09-01, Stony Brook University, Department of Economics.
    4. Ghazala Azmat & Nagore Iriberri, 2009. "The Importance of Relative Performance Feedback Information: Evidence from a Natural Experiment using High School Students," CEP Discussion Papers dp0915, Centre for Economic Performance, LSE.
    5. Shyam Sunder & Karim Jamal, 2006. "Regulation, Competition and Independence in a Certification Society: Financial Reports Vs. Baseball Cards," Yale School of Management Working Papers amz2578, Yale School of Management, revised 01 Jun 2007.
    6. Ed Hopkins & Tatiana Kornienko, 2005. "Methods of Comparison in Games of Status," ESE Discussion Papers 138, Edinburgh School of Economics, University of Edinburgh.
    7. Pradeep Dubey & John Geanakoplos, 2009. "Grading Exams: 100, 99, 98,... or A, B, C?," Levine's Working Paper Archive 814577000000000361, David K. Levine.
    8. Pradeep K. Dubey & John Geanakoplos & Ori Haimanko, 2005. "Prizes versus Wages with Envy and Pride," Cowles Foundation Discussion Papers 1537, Cowles Foundation for Research in Economics, Yale University.
    9. Pradeep Dubey & John Geanakoplos, 2009. "Grading Exams: 100, 99, 98,...or A, B, C?," Cowles Foundation Discussion Papers 1710, Cowles Foundation for Research in Economics, Yale University.

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