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

Matthew Gentry, Tong Li and Jingfeng Lu

Games and Economic Behavior, 2015, vol. 94, issue C, 214-221

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.

Keywords: Constant absolute risk aversion (CARA); Constant relative risk aversion (CRRA); First price auction; Initial wealth; Monotone equilibrium (search for similar items in EconPapers)
JEL-codes: C7 D7 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Working Paper: Existence of monotone equilibrium in first price auctions with private risk aversion and private initial wealth (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:94:y:2015:i:c:p:214-221

DOI: 10.1016/j.geb.2015.07.003

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