IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v63y2016icp1-9.html
   My bibliography  Save this article

An envelope approach to tournament design

Author

Listed:
  • Ewerhart, Christian

Abstract

Optimal rank-order tournaments have traditionally been studied using a first-order approach. The present analysis relies instead on the construction of an “upper envelope” over all incentive compatibility conditions. It turns out that the first-order approach is not innocuous. For example, in contrast to the traditional understanding, tournaments may be dominated by piece rates even if workers are risk-neutral. The paper also offers a strikingly simple characterization of the optimal tournament for quadratic costs and CARA utility, as well as an extension to large tournaments.

Suggested Citation

  • Ewerhart, Christian, 2016. "An envelope approach to tournament design," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 1-9.
    • Handle: RePEc:eee:mateco:v:63:y:2016:i:c:p:1-9
    DOI: 10.1016/j.jmateco.2015.11.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406815001445
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2015.11.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    3. Christian Ewerhart, 2015. "Mixed equilibria in Tullock contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 59-71, September.
    4. Canice Prendergast, 1999. "The Provision of Incentives in Firms," Journal of Economic Literature, American Economic Association, vol. 37(1), pages 7-63, March.
    5. Araujo, Aloisio & Moreira, Humberto, 2001. "A general Lagrangian approach for non-concave moral hazard problems," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 17-39, February.
    6. Robert Akerlof & Richard Holden, 2012. "The nature of tournaments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 289-313, October.
    7. Philipp Renner & Karl Schmedders, 2015. "A Polynomial Optimization Approach to Principal–Agent Problems," Econometrica, Econometric Society, vol. 83, pages 729-769, March.
    8. Gürtler, Oliver, 2011. "The first-order approach in rank-order tournaments," Economics Letters, Elsevier, vol. 111(3), pages 185-187, June.
    9. Steffen Altmann & Armin Falk & Matthias Wibral, 2012. "Promotions and Incentives: The Case of Multistage Elimination Tournaments," Journal of Labor Economics, University of Chicago Press, vol. 30(1), pages 149-174.
    10. Pierre Chaigneau & Alex Edmans & Daniel Gottlieb, 2014. "The Generalized Informativeness Principle," NBER Working Papers 20729, National Bureau of Economic Research, Inc.
    11. 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.
    12. Dilip Mookherjee, 1984. "Optimal Incentive Schemes with Many Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(3), pages 433-446.
    13. Budde, Jörg, 2009. "Information in tournaments under limited liability," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 59-72, January.
    14. O'Keeffe, Mary & Viscusi, W Kip & Zeckhauser, Richard J, 1984. "Economic Contests: Comparative Reward Schemes," Journal of Labor Economics, University of Chicago Press, vol. 2(1), pages 27-56, January.
    15. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    16. Margaret A. Meyer, 1992. "Biased Contests and Moral Hazard: Implications for Career Profiles," Annals of Economics and Statistics, GENES, issue 25-26, pages 165-187.
    17. William Chan & Pascal Courty & Li Hao, 2009. "Suspense: Dynamic Incentives in Sports Contests," Economic Journal, Royal Economic Society, vol. 119(534), pages 24-46, January.
    18. Waldman, Michael, 2013. "Classic promotion tournaments versus market-based tournaments," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 198-210.
    19. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    20. Hvide, Hans K. & Kristiansen, Eirik G., 2003. "Risk taking in selection contests," Games and Economic Behavior, Elsevier, vol. 42(1), pages 172-179, January.
    21. Bull, Clive & Schotter, Andrew & Weigelt, Keith, 1987. "Tournaments and Piece Rates: An Experimental Study," Journal of Political Economy, University of Chicago Press, vol. 95(1), pages 1-33, February.
    22. Barry J. Nalebuff & Joseph E. Stiglitz, 1983. "Prices and Incentives: Towards a General Theory of Compensation and Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 21-43, Spring.
    23. Ajay Kalra & Mengze Shi, 2001. "Designing Optimal Sales Contests: A Theoretical Perspective," Marketing Science, INFORMS, vol. 20(2), pages 170-193, December.
    24. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    25. Hisaki Kono & Nobuyuki Yagi, 2008. "Heterogeneous Contests And Less Informative Signals," The Japanese Economic Review, Japanese Economic Association, vol. 59(1), pages 113-126, March.
    26. repec:adr:anecst:y:1992:i:25-26:p:08 is not listed on IDEAS
    27. Derek Clark & Christian Riis, 2001. "Rank-order tournaments and selection," Journal of Economics, Springer, vol. 73(2), pages 167-191, June.
    28. Sinclair-Desgagne, Bernard, 1994. "The First-Order Approach to Multi-signal Principal-Agent Problems," Econometrica, Econometric Society, vol. 62(2), pages 459-466, March.
    29. Kadan, Ohad & Swinkels, Jeroen M., 2013. "On the moral hazard problem without the first-order approach," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2313-2343.
    30. John R. Conlon, 2009. "Two New Conditions Supporting the First-Order Approach to Multisignal Principal-Agent Problems," Econometrica, Econometric Society, vol. 77(1), pages 249-278, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "Tournament rewards and heavy tails," Journal of Economic Theory, Elsevier, vol. 190(C).
    2. Christian Ewerhart & Marco Serena, 2023. "On the (im-)possibility of representing probability distributions as a difference of i.i.d. noise terms," ECON - Working Papers 428, Department of Economics - University of Zurich, revised Oct 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "Tournament rewards and heavy tails," Journal of Economic Theory, Elsevier, vol. 190(C).
    2. Kirkegaard, René, 2017. "Moral hazard and the spanning condition without the first-order approach," Games and Economic Behavior, Elsevier, vol. 102(C), pages 373-387.
    3. Tor Eriksson & Sabrina Teyssier & Marie‐Claire Villeval, 2009. "Self‐Selection And The Efficiency Of Tournaments," Economic Inquiry, Western Economic Association International, vol. 47(3), pages 530-548, July.
    4. Fleckinger, Pierre, 2012. "Correlation and relative performance evaluation," Journal of Economic Theory, Elsevier, vol. 147(1), pages 93-117.
    5. Waldman, Michael, 2013. "Classic promotion tournaments versus market-based tournaments," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 198-210.
    6. Loukas Balafoutas & E. Glenn Dutcher & Florian Lindner & Dmitry Ryvkin, 2017. "The Optimal Allocation Of Prizes In Tournaments Of Heterogeneous Agents," Economic Inquiry, Western Economic Association International, vol. 55(1), pages 461-478, January.
    7. repec:eee:labchp:v:3:y:1999:i:pb:p:2373-2437 is not listed on IDEAS
    8. Josse Delfgaauw & Robert Dur & Arjan Non & Willem Verbeke, 2015. "The Effects of Prize Spread and Noise in Elimination Tournaments: A Natural Field Experiment," Journal of Labor Economics, University of Chicago Press, vol. 33(3), pages 521-569.
    9. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    10. Jung, Jin Yong, 2022. "Effects of changes in preferences in moral hazard problems," Journal of Economic Theory, Elsevier, vol. 205(C).
    11. Niladri Syam & James Hess & Ying Yang, 2013. "Sales contests versus quotas with imbalanced territories," Marketing Letters, Springer, vol. 24(3), pages 229-244, September.
    12. Sun, Sophia Li & Habib, Ahsan, 2020. "Determinants and consequences of tournament incentives: A survey of the literature in accounting and finance," Research in International Business and Finance, Elsevier, vol. 54(C).
    13. Budde, Jörg, 2009. "Information in tournaments under limited liability," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 59-72, January.
    14. Gill, David & Stone, Rebecca, 2010. "Fairness and desert in tournaments," Games and Economic Behavior, Elsevier, vol. 69(2), pages 346-364, July.
    15. Chaigneau, Pierre & Edmans, Alex & Gottlieb, Daniel, 2019. "The informativeness principle without the first-order approach," Games and Economic Behavior, Elsevier, vol. 113(C), pages 743-755.
    16. Jed DeVaro & Antti Kauhanen, 2016. "An “Opposing Responses” Test of Classic versus Market-Based Promotion Tournaments," Journal of Labor Economics, University of Chicago Press, vol. 34(3), pages 747-779.
    17. Bernd Irlenbusch, 2006. "Experimental perspectives on incentives in organisations," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(1), pages 1-24, February.
    18. Tor Eriksson & Sabrina Teyssier & Marie Claire Villeval, 2006. "Effort Self-Selection and the Efficiency of Tournaments," Post-Print halshs-00142876, HAL.
    19. Zhen Wang & Tomislav Vukina, 2017. "Welfare effects of payment truncation in piece rate tournaments," Journal of Economics, Springer, vol. 120(3), pages 219-249, April.
    20. Bernd Frick, 2003. "Contest Theory and Sport," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 19(4), pages 512-529, Winter.
    21. Brookins, Philip & Jindapon, Paan, 2021. "Risk preference heterogeneity in group contests," Journal of Mathematical Economics, Elsevier, vol. 95(C).

    More about this item

    Keywords

    Rank-order tournaments; First-order approach; Envelope theorem;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • L23 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Organization of Production

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:63:y:2016:i:c:p:1-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.