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

Gentry, Matthew, Li, Tong and Lu, Jingfeng (2015) Existence of monotone equilibrium in first price auctions with private risk aversion and private initial wealth. Games and Economic Behavior, 94. pp. 214-221. ISSN 0899-8256

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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.

Item Type:	Article
Official URL:	http://www.journals.elsevier.com/games-and-economi...
Additional Information:	© 2015 Elsevier Inc.
Divisions:	Economics
Subjects:	H Social Sciences > H Social Sciences (General) H Social Sciences > HB Economic Theory Q Science > QA Mathematics
JEL classification:	C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory D - Microeconomics > D7 - Analysis of Collective Decision-Making
Date Deposited:	14 Apr 2016 08:28
Last Modified:	14 Sep 2024 06:55
URI:	http://eprints.lse.ac.uk/id/eprint/66100

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