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Constant risk aversion in stochastic contests with exponential completion times

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  • Pelin G. Canbolat
  • Uriel G. Rothblum

Abstract

This article analyzes a class of stochastic contests among multiple players under risk‐averse exponential utility. In these contests, players compete over the completion of a task by simultaneously deciding on their investment, which determines how fast they complete the task. The completion time of the task for each player is assumed to be an exponentially distributed random variable with rate linear in the player's investment and the completion times of different players are assumed to be stochastically independent. The player that completes the task first earns a prize whereas the remaining players earn nothing. The article establishes a one‐to‐one correspondence between the Nash equilibrium of this contest with respect to risk‐averse exponential utilities and the nonnegative solution of a nonlinear equation. Using the properties of the latter, it proves the existence and the uniqueness of the Nash equilibrium, and provides an efficient method to compute it. It exploits the resulting representation of the equilibrium investments to determine the effects of risk aversion and the differences between the outcome of the Nash equilibrium and that of a centralized version.© 2016 Wiley Periodicals, Inc. Naval Research Logistics 66:4–14, 2019

Suggested Citation

  • Pelin G. Canbolat & Uriel G. Rothblum, 2019. "Constant risk aversion in stochastic contests with exponential completion times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 4-14, February.
    • Handle: RePEc:wly:navres:v:66:y:2019:i:1:p:4-14
    DOI: 10.1002/nav.21727
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    References listed on IDEAS

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    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.
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    2. Jens Gudmundsson & Jens Leth Hougaard, 2020. "Enabling reciprocity through blockchain design," IFRO Working Paper 2020/14, University of Copenhagen, Department of Food and Resource Economics, revised 09 Feb 2021.
    3. Liu, Yong & Liu, Shulin, 2019. "Effects of risk aversion on all-pay auction with reimbursement," Economics Letters, Elsevier, vol. 185(C).

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