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Optimal scrutiny in multi-period promotion tournaments

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  • Dubey, Pradeep
  • Haimanko, Ori

Abstract

Consider a principal who hires heterogeneous agents to work for him over T periods, without prior knowledge of their respective skills, and intends to promote one of them at the end. In each period the agents choose effort levels and produce random outputs, independently of each other, and are fully informed of the past history of outputs. The principal's major objective is to maximize the total expected output, but he may also put some weight on detecting the higher-skilled agent for promotion. To this end, he randomly samples n out of the T periods and awards the promotion to the agent who produces more on the sample. This determines an extensive form game Gamma (T,n), which we analyze for its subgame perfect equilibria in behavioral strategies. We show that the principal will do best to always choose a small sample size n. More precisely, if eta(T) is the maximal optimal sample size, then eta(T)/T approaches 0 as T approaches infinity.
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Suggested Citation

  • Dubey, Pradeep & Haimanko, Ori, 2003. "Optimal scrutiny in multi-period promotion tournaments," Games and Economic Behavior, Elsevier, vol. 42(1), pages 1-24, January.
  • Handle: RePEc:eee:gamebe:v:42:y:2003:i:1:p:1-24
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    References listed on IDEAS

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    1. 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 841-864, October.
    2. Dubey, Pradeep & Kaneko, Mamoru, 1985. "Information patterns and Nash equilibria in extensive games -- II," Mathematical Social Sciences, Elsevier, vol. 10(3), pages 247-262, December.
    3. 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 349-364, June.
    4. Cowen, Tyler & Glazer, Amihai, 1996. "More monitoring can induce less effort," Journal of Economic Behavior & Organization, Elsevier, vol. 30(1), pages 113-123, July.
    5. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-715, September.
    6. Dubey, Pradeep & Kaneko, Mamoru, 1984. "Information patterns and Nash equilibria in extensive games: 1," Mathematical Social Sciences, Elsevier, vol. 8(2), pages 111-139, October.
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    Cited by:

    1. Pradeep Dubey & Siddhartha Sahi, 2009. "The Allocation of a Prize," Department of Economics Working Papers 09-01, Stony Brook University, Department of Economics.
    2. Yohan Pelosse, 2014. "Dynamic Difference-Form Contests," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(3), pages 401-426, June.
    3. Gershkov, Alex & Perry, Motty, 2009. "Tournaments with midterm reviews," Games and Economic Behavior, Elsevier, vol. 66(1), pages 162-190, May.
    4. 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, revised Dec 2005.
    5. Pradeep Dubey & Siddhartha Sahi, 2016. "Eliciting performance: deterministic versus proportional prizes," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 239-267, March.
    6. Dubey, Pradeep & Wu, Chien-wei, 2001. "Competitive prizes: when less scrutiny induces more effort," Journal of Mathematical Economics, Elsevier, vol. 36(4), pages 311-336, December.
    7. repec:ebl:ecbull:v:12:y:2005:i:13:p:1-7 is not listed on IDEAS
    8. Kam Ki Tang & Leopoldo Yanes, 2009. "The hierarchical structure of the firm: a geometric perspective," Prague Economic Papers, University of Economics, Prague, vol. 2009(2), pages 156-175.
    9. Yaakov Kareev & Judith Avrahami, 2006. "Choosing Between Adaptive Agents: Some Unexpected Implications of Level of Scrutiny," Levine's Bibliography 321307000000000521, UCLA Department of Economics.
    10. Kam Ki Tang & Rodney Beard & Evelyn Ng & Leopoldo Yanes, 2005. "The hierarchical structure of a firm: a geometric approach," Economics Bulletin, AccessEcon, vol. 12(13), pages 1-7.
    11. Pradeep Dubey & Siddhartha Sah, 2012. "The Allocation of a Prize (Expanded)," Department of Economics Working Papers 12-02, Stony Brook University, Department of Economics.
    12. Pradeep Dubey & John Geanakoplos, 2014. "Games with Money and Status: How Best to Incentivize Work," Cowles Foundation Discussion Papers 1954, Cowles Foundation for Research in Economics, Yale University.
    13. Yaakov Kareev & Judith Avrahami, 2006. "Choosing Between Adaptive Agents: Some Unexpected Implications of Level of Scrutiny," Discussion Paper Series dp436, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    14. G├╝rtler, Oliver, 2006. "Job Promotion Tournaments and Imperfect Recall," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 112, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • J41 - Labor and Demographic Economics - - Particular Labor Markets - - - Labor Contracts

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