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Stochastic Contests with Linex Utility Functions

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  • Pelin G. Canbolat

Abstract

In this paper, we analyze the Nash equilibrium in a class of winner-takes-all stochastic contests among players with linear-exponential (linex) utility functions. In this contest, players are required to make upfront investments, which collectively determine their winning probabilities. We first show that a Nash equilibrium for such a contest exists and is unique, then set the equilibrium conditions, and study the properties of these conditions to gain insights into the structure of equilibrium. We show that the total equilibrium investment is bounded below and above, that the equilibrium has a cut characterization with respect to wealth, and that wealthier players invest more. The latter implies that richer is likely to get richer. For the special case with identical players, we show that an increase in the wealth or a decrease in the weight on the nonlinear component of the linex utility function results in an increase in the equilibrium investment.

Suggested Citation

  • Pelin G. Canbolat, 2019. "Stochastic Contests with Linex Utility Functions," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 7(1), pages 113-128, June.
    • Handle: RePEc:anm:alpnmr:v:7:y:2019:i:1:p:113-128
    DOI: http://dx.doi.org/10.17093/alphanumeric.456860
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    References listed on IDEAS

    as
    1. Richard Cornes & Roger Hartley, 2012. "Risk aversion in symmetric and asymmetric contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 247-275, October.
    2. Denuit, Michel M. & Eeckhoudt, Louis & Schlesinger, Harris, 2013. "When Ross meets Bell: The linex utility function," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 177-182.
    3. Nicolas Treich, 2010. "Risk-aversion and prudence in rent-seeking games," Public Choice, Springer, vol. 145(3), pages 339-349, December.
    4. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    5. Pelin G. Canbolat & Boaz Golany & Inbal Mund & Uriel G. Rothblum, 2012. "A Stochastic Competitive R&D Race Where “Winner Takes All”," Operations Research, INFORMS, vol. 60(3), pages 700-715, June.
    6. Takeshi Yamazaki, 2009. "The uniqueness of pure-strategy Nash equilibrium in rent-seeking games with risk-averse players," Public Choice, Springer, vol. 139(3), pages 335-342, June.
    7. Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-638, May.
    8. Cornes, Richard & Hartley, Roger, 2003. "Risk Aversion, Heterogeneity and Contests," Public Choice, Springer, vol. 117(1-2), pages 1-25, October.
    9. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
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    More about this item

    Keywords

    Game Theory; Linear-Exponential Utility; Stochastic Contests; Winner-Takes-All;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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