[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v44y2008i11p1219-1231.html
   My bibliography  Save this article

Optimal risk taking in an uneven tournament game with risk averse players

Author

Listed:
  • Kräkel, Matthias
Abstract
We analyze the optimal choice of risk in a two-stage tournament game between two players that have different concave utility functions. At the first stage, both players simultaneously choose risk. At the second stage, both observe overall risk and simultaneously decide on effort or investment. The results show that those two effects which mainly determine risk taking - an effort effect and a likelihood effect - are strictly interrelated. This finding sharply contrasts with existing results on risk taking in tournament games with symmetric equilibrium efforts where such linkage can never arise. Conditions are derived under which this linkage leads to a reversed likelihood effect so that the favorite (underdog) can increase his winning probability by increasing (decreasing) risk which is impossible in a completely symmetric setting.

Suggested Citation

  • Kräkel, Matthias, 2008. "Optimal risk taking in an uneven tournament game with risk averse players," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1219-1231, December.
    • Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1219-1231
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4068(08)00014-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. J. Atsu Amegashie, 2009. "American Idol: should it be a singing contest or a popularity contest?," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 33(4), pages 265-277, November.
    3. Matthias Kräkel & Dirk Sliwka, 2004. "Risk Taking in Asymmetric Tournaments," German Economic Review, Verein für Socialpolitik, vol. 5(1), pages 103-116, February.
    4. Christian Grund & Oliver Gurtler, 2005. "An empirical study on risk-taking in tournaments," Applied Economics Letters, Taylor & Francis Journals, vol. 12(8), pages 457-461.
    5. Chevalier, Judith & Ellison, Glenn, 1997. "Risk Taking by Mutual Funds as a Response to Incentives," Journal of Political Economy, University of Chicago Press, vol. 105(6), pages 1167-1200, December.
    6. Warneryd, Karl, 2000. "In Defense of Lawyers: Moral Hazard as an Aid to Cooperation," Games and Economic Behavior, Elsevier, vol. 33(1), pages 145-158, October.
    7. Gibbons, Robert, 2005. "Four forma(lizable) theories of the firm?," Journal of Economic Behavior & Organization, Elsevier, vol. 58(2), pages 200-245, October.
    8. Robert Gibbons & Kevin J. Murphy, 1990. "Relative Performance Evaluation for Chief Executive Officers," ILR Review, Cornell University, ILR School, vol. 43(3), pages 30, April.
    9. Hans K. Hvide, 2002. "Tournament Rewards and Risk Taking," Journal of Labor Economics, University of Chicago Press, vol. 20(4), pages 877-898, October.
    10. Knoeber, Charles R & Thurman, Walter N, 1994. "Testing the Theory of Tournaments: An Empirical Analysis of Broiler Production," Journal of Labor Economics, University of Chicago Press, vol. 12(2), pages 155-179, April.
    11. 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.
    12. Anil Gaba & Ajay Kalra, 1999. "Risk Behavior in Response to Quotas and Contests," Marketing Science, INFORMS, vol. 18(3), pages 417-434.
    13. Konrad, Kai A., 2007. "Strategy in contests: an introduction [Strategie in Turnieren – eine Einführung]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, WZB Berlin Social Science Center.
    14. Stefan Szymanski, 2010. "The Economic Design of Sporting Contests," Palgrave Macmillan Books, in: The Comparative Economics of Sport, chapter 1, pages 1-78, Palgrave Macmillan.
    15. Hvide, Hans K. & Kristiansen, Eirik G., 2003. "Risk taking in selection contests," Games and Economic Behavior, Elsevier, vol. 42(1), pages 172-179, January.
    16. Taylor, Jonathan, 2003. "Risk-taking behavior in mutual fund tournaments," Journal of Economic Behavior & Organization, Elsevier, vol. 50(3), pages 373-383, March.
    17. Avinash Dixit, 2008. "Strategic Behavior in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 431-438, Springer.
    18. Dragon, Robert & Garvey, Gerald T. & Turnbull, Geoffrey K., 1996. "A collective tournament," Economics Letters, Elsevier, vol. 50(2), pages 223-227, February.
    19. Anja Schöttner, 2008. "Fixed-prize tournaments versus first-price auctions in innovation contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 57-71, April.
    20. George Baker & Michael Gibbs & Bengt Holmstrom, 1994. "The Wage Policy of a Firm," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(4), pages 921-955.
    21. repec:ebl:ecbull:v:28:y:2007:i:16:p:a0 is not listed on IDEAS
    22. Richard Schmalensee, 1976. "A Model of Promotional Competition in Oligopoly," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(3), pages 493-507.
    23. Muller, Sigrid M. & Machina, Mark J., 1987. "Moment preferences and polynomial utility," Economics Letters, Elsevier, vol. 23(4), pages 349-353.
    24. Kong-Pin Chen, 2003. "Sabotage in Promotion Tournaments," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 19(1), pages 119-140, April.
    25. Brown, Keith C & Harlow, W V & Starks, Laura T, 1996. "Of Tournaments and Temptations: An Analysis of Managerial Incentives in the Mutual Fund Industry," Journal of Finance, American Finance Association, vol. 51(1), pages 85-110, March.
    26. Steven Tadelis, 2002. "The Market for Reputations as an Incentive Mechanism," Journal of Political Economy, University of Chicago Press, vol. 110(4), pages 854-882, August.
    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. Madalina Anghel & Aurel Diaconu & Marius Popovici, 2016. "Theoretical considerations regarding risk analysis models," Romanian Statistical Review Supplement, Romanian Statistical Review, vol. 64(9), pages 64-72, September.
    2. Lindner, Florian & Kirchler, Michael & Rosenkranz, Stephanie & Weitzel, Utz, 2021. "Social Motives and Risk-Taking in Investment Decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    3. Czerny, Achim I. & Fosgerau, Mogens & Jost, Peter-J. & van Ommeren, Jos N., 2019. "Why pay for jobs (and not for tasks)?," Journal of Economic Behavior & Organization, Elsevier, vol. 168(C), pages 419-433.
    4. J. Atsu Amegashie, 2009. "American Idol: should it be a singing contest or a popularity contest?," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 33(4), pages 265-277, November.
    5. Spencer Bastani & Thomas Giebe & Oliver Gürtler, 2019. "A General Framework for Studying Contests," CESifo Working Paper Series 7993, CESifo.
    6. Suzuki, Toru, 2012. "Competitive problem solving and the optimal prize schemes," Games and Economic Behavior, Elsevier, vol. 75(2), pages 1009-1013.
    7. Kräkel, Matthias & Nieken, Petra & Przemeck, Judith, 2014. "Risk taking and investing in electoral competition," European Journal of Political Economy, Elsevier, vol. 33(C), pages 98-120.
    8. Kräkel, Matthias & Schöttner, Anja, 2010. "Technology choice, relative performance pay, and worker heterogeneity," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 748-758, December.
    9. Gürtler, Oliver & Struth, Lennart & Thon, Max, 2023. "Competition and risk-taking," European Economic Review, Elsevier, vol. 160(C).
    10. Grunewald, Andreas & Kräkel, Matthias, 2017. "Fake News," IZA Discussion Papers 11207, Institute of Labor Economics (IZA).
    11. Kräkel, Matthias & Schöttner, Anja, 2010. "Technology Choice and Incentives under Relative Performance Schemes," Bonn Econ Discussion Papers 10/2010, University of Bonn, Bonn Graduate School of Economics (BGSE).
    12. Grossmann, Martin, 2014. "Uncertain contest success function," European Journal of Political Economy, Elsevier, vol. 33(C), pages 134-148.
    13. Bernd Frick & Oliver Gürtler & Joachim Prinz, 2008. "Anreize in Turnieren mit heterogenen Teilnehmern — Eine empirische Untersuchung mit Daten aus der Fußball-Bundesliga," Schmalenbach Journal of Business Research, Springer, vol. 60(4), pages 385-405, June.
    14. Petra Nieken, 2010. "On the Choice of Risk and Effort in Tournaments—Experimental Evidence," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 19(3), pages 811-840, September.
    15. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.

    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. Kräkel, Matthias & Nieken, Petra & Przemeck, Judith, 2014. "Risk taking and investing in electoral competition," European Journal of Political Economy, Elsevier, vol. 33(C), pages 98-120.
    2. Mueller-Langer, Frank & Andreoli-Versbach, Patrick, 2013. "Leading-effect vs. Risk-taking in Dynamic Tournaments: Evidence from a Real-life Randomized Experiment," Discussion Papers in Economics 15452, University of Munich, Department of Economics.
    3. J. Atsu Amegashie, 2009. "American Idol: should it be a singing contest or a popularity contest?," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 33(4), pages 265-277, November.
    4. Mueller-Langer Frank & Andreoli-Versbach Patrick, 2017. "Leading-Effect, Risk-Taking and Sabotage in Two-Stage Tournaments: Evidence from a Natural Experiment," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 237(1), pages 1-28, February.
    5. Gürtler, Oliver & Kräkel, Matthias, 2010. "Optimal tournament contracts for heterogeneous workers," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 180-191, August.
    6. Kräkel, Matthias & Schöttner, Anja, 2010. "Technology Choice and Incentives under Relative Performance Schemes," Bonn Econ Discussion Papers 10/2010, University of Bonn, Bonn Graduate School of Economics (BGSE).
    7. Kräkel, Matthias & Schöttner, Anja, 2010. "Technology choice, relative performance pay, and worker heterogeneity," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 748-758, December.
    8. Nieken, Petra & Sliwka, Dirk, 2010. "Risk-taking tournaments - Theory and experimental evidence," Journal of Economic Psychology, Elsevier, vol. 31(3), pages 254-268, June.
    9. Matthias Kräkel, 2014. "Sandbagging," Journal of Sports Economics, , vol. 15(3), pages 263-284, June.
    10. Eriksen, Kristoffer W. & Kvaløy, Ola, 2014. "Myopic risk-taking in tournaments," Journal of Economic Behavior & Organization, Elsevier, vol. 97(C), pages 37-46.
    11. Matthias Kräkel, 2014. "Optimal seedings in elimination tournaments revisited," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 77-91, April.
    12. Konrad, Kai A., 2007. "Strategy in contests: an introduction [Strategie in Turnieren – eine Einführung]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, WZB Berlin Social Science Center.
    13. Nieken, Petra & Stegh, Michael, 2010. "Incentive Effects in Asymmetric Tournaments Empirical Evidence from the German Hockey League," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 305, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    14. Gürtler, Oliver & Struth, Lennart & Thon, Max, 2023. "Competition and risk-taking," European Economic Review, Elsevier, vol. 160(C).
    15. Kräkel, Matthias & Nieken, Petra, 2015. "Relative performance pay in the shadow of crisis," European Economic Review, Elsevier, vol. 74(C), pages 244-268.
    16. Cui, Xuegang & Feltovich, Nick & Zhang, Kun, 2022. "Incentive schemes, framing, and market behaviour: Evidence from an asset-market experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 197(C), pages 301-324.
    17. Usvitskiy, Alexander, 2022. "Strategic risk-taking in dynamic contests," Journal of Economic Behavior & Organization, Elsevier, vol. 198(C), pages 511-534.
    18. Anil Gaba & Ilia Tsetlin & Robert L. Winkler, 2004. "Modifying Variability and Correlations in Winner-Take-All Contests," Operations Research, INFORMS, vol. 52(3), pages 384-395, June.
    19. Grund, Christian & Höcker, Jan & Zimmermann, Stefan, 2010. "Risk Taking Behavior in Tournaments: Evidence from the NBA," IZA Discussion Papers 4812, Institute of Labor Economics (IZA).
    20. Markus LANG & Alexander RATHKE & Marco RUNKEL, 2010. "The Economic Consequences Of Foreigner Rules In National Sports Leagues," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 31, pages 47-64.

    More about this item

    Keywords

    Asymmetric equilibria Rank-order tournaments Risk taking;

    JEL classification:

    • M5 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • J3 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs

    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:44:y:2008:i:11:p:1219-1231. 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.