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

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  • 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.

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  • 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
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    2. 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.
    3. Spencer Bastani & Thomas Giebe & Oliver Gürtler, 2019. "A General Framework for Studying Contests," CESifo Working Paper Series 7993, CESifo.
    4. 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.
    5. Gürtler, Oliver & Struth, Lennart & Thon, Max, 2023. "Competition and risk-taking," European Economic Review, Elsevier, vol. 160(C).
    6. 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.
    7. 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.
    8. Suzuki, Toru, 2012. "Competitive problem solving and the optimal prize schemes," Games and Economic Behavior, Elsevier, vol. 75(2), pages 1009-1013.
    9. 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.
    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.

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    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

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