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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.

Suggested Citation

  • Pradeep Dubey & John Geanakoplos, 2005. "Grading in Games of Status: Marking Exams and Setting Wages," Cowles Foundation Discussion Papers 1544, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1544
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    Cited by:

    1. Bruno S. Frey & Susanne Neckermann, 2008. "Awards: A view from psychological economics," IEW - Working Papers 357, Institute for Empirical Research in Economics - University of Zurich.
    2. Pradeep Dubey & John Geanakoplos & Ori Haimanko, 2013. "Prizes Versus Wages With Envy And Pride," The Japanese Economic Review, Japanese Economic Association, vol. 64(1), pages 98-121, March.
    3. Sheheryar Banuri & Katarina Dankova & Philip Keefer, 2017. "It's not all fun and games: Feedback, task motivation, and effort," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 17-10, School of Economics, University of East Anglia, Norwich, UK..
    4. Islam,Asad & Kwon,Sungoh & Masood,Eema & Prakash,Nishith & Sabarwal,Shwetlena & Saraswat,Deepak, 2020. "When Goal-Setting Forges Ahead but Stops Short," Policy Research Working Paper Series 9406, The World Bank.
    5. Pradeep Dubey & Siddhartha Sahi, 2009. "The Allocation of a Prize," Department of Economics Working Papers 09-01, Stony Brook University, Department of Economics.
    6. Azmat, Ghazala & Iriberri, Nagore, 2010. "The importance of relative performance feedback information: Evidence from a natural experiment using high school students," Journal of Public Economics, Elsevier, vol. 94(7-8), pages 435-452, August.
    7. Benny Moldovanu & Aner Sela & Xianwen Shi, 2007. "Contests for Status," Journal of Political Economy, University of Chicago Press, vol. 115(2), pages 338-363.
    8. Dessi, Roberta & Miquel-Florensa, Josepa, 2013. "When to Pay More: Incentives, Culture and Status in Principal‐ Agent Interactions," TSE Working Papers 13-413, Toulouse School of Economics (TSE).
    9. 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.
    10. 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.
    11. Michael Kosfeld & Susanne Neckermann, 2011. "Getting More Work for Nothing? Symbolic Awards and Worker Performance," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 86-99, August.
    12. Dubey, Pradeep & Geanakoplos, John, 2010. "Grading exams: 100,99,98,... or A,B,C?," Games and Economic Behavior, Elsevier, vol. 69(1), pages 72-94, May.
    13. 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.
    14. Bruno S. Frey, 2010. "Geld oder Anerkennung? Zur Ökonomik der Auszeichnungen," Perspektiven der Wirtschaftspolitik, Verein für Socialpolitik, vol. 11(1), pages 1-15, February.
    15. Depoorter Ben & Holland Adam & Somerstein Elizabeth, 2009. "Copyright Abolition and Attribution," Review of Law & Economics, De Gruyter, vol. 5(3), pages 1063-1080, December.
    16. 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.
    17. Bruno S. Frey & Susanne Neckermann, 2008. "Awards: Questioning Popular Notions," CREMA Working Paper Series 2008-14, Center for Research in Economics, Management and the Arts (CREMA).
    18. Subrato Banerjee, 2020. "Effect of reduced opportunities on bargaining outcomes: an experiment with status asymmetries," Theory and Decision, Springer, vol. 89(3), pages 313-346, October.
    19. Ed Hopkins & Tatiana Kornienko, 2006. "Methods of Comparison in Games of Status," Edinburgh School of Economics Discussion Paper Series 138, Edinburgh School of Economics, University of Edinburgh.

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    More about this item

    Keywords

    Status; Grading; Incentives; Education; Exams; Wages;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • I20 - Health, Education, and Welfare - - Education - - - General
    • I30 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General

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