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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.

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
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    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. 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, pages 265-277.
    3. Suzuki, Toru, 2012. "Competitive problem solving and the optimal prize schemes," Games and Economic Behavior, Elsevier, vol. 75(2), pages 1009-1013.
    4. 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.
    5. Grossmann, Martin, 2014. "Uncertain contest success function," European Journal of Political Economy, Elsevier, vol. 33(C), pages 134-148.

    More about this item

    Keywords

    Asymmetric equilibria Rank-order tournaments Risk taking;

    JEL classification:

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

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