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Existence of monotone equilibrium in first price auctions with private risk aversion and private initial wealth

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  • Gentry, Matthew
  • Li, Tong
  • Lu, Jingfeng

Abstract

In this paper, we study the existence of monotone equilibrium in first price auctions where bidders have a three-dimensional private type, i.e. their private values, degrees of risk aversion and initial wealth. Bidders' utility functions belong to the class of constant relative risk aversion (CRRA) or constant absolute risk aversion (CARA). The bidders' types are independent across bidders, while a bidder's private value, initial wealth and degree of risk aversion are allowed to be correlated. We show that a monotone equilibrium always exists in a general setting allowing for asymmetric bidders. Moreover, with symmetric bidders, a symmetric monotone equilibrium strategy must exist. A bidder's equilibrium strategy increases with bidders' private values and degrees of risk aversion. When bidders have CRRA utility, equilibrium bids decrease with initial wealth; when bidders have CARA utility, equilibrium bids are invariant to initial wealth.

Suggested Citation

  • Gentry, Matthew & Li, Tong & Lu, Jingfeng, 2015. "Existence of monotone equilibrium in first price auctions with private risk aversion and private initial wealth," Games and Economic Behavior, Elsevier, vol. 94(C), pages 214-221.
    • Handle: RePEc:eee:gamebe:v:94:y:2015:i:c:p:214-221
    DOI: 10.1016/j.geb.2015.07.003
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    Cited by:

    1. Muhammad Ejaz & Nisho Rani & Muhammad Ramzan Sheikh, 2023. "First Price Sealed-Bid Auctions with Bidders’ Heterogeneous Risk Behavior: An Adversarial Risk Analysis Approach," Decision Analysis, INFORMS, vol. 20(3), pages 231-241, September.
    2. Muhammad Ejaz & Stephen Joe & Chaitanya Joshi, 2021. "Adversarial Risk Analysis for Auctions Using Mirror Equilibrium and Bayes Nash Equilibrium," Decision Analysis, INFORMS, vol. 18(3), pages 185-202, September.
    3. He, Wei & Sun, Yeneng, 2019. "Pure-strategy equilibria in Bayesian games," Journal of Economic Theory, Elsevier, vol. 180(C), pages 11-49.
    4. Li, Zhen & Yue, Jinfeng & Kuo, Ching-Chung, 2018. "Design of discrete Dutch auctions with consideration of time," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1159-1171.

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    More about this item

    Keywords

    Constant absolute risk aversion (CARA); Constant relative risk aversion (CRRA); First price auction; Initial wealth; Monotone equilibrium;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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