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Numerical Computation of Equilibrium Bid Functions in a First-Price Auction with Heterogeneous Risk Attitudes

Published online by Cambridge University Press:  14 March 2025

Mark V Van Boening ,
Stephen J. Rassenti  and
Vernon L. Smith
Mark V Van Boening
Affiliation:
Department of Economics and Finance, University of Mississippi
Stephen J. Rassenti
Affiliation:
Economic Science Laboratory, 116 McClelland Hall, University of Arizona, Tucson, AZ 85721
Vernon L. Smith
Affiliation:
Economic Science Laboratory, 116 McClelland Hall, University of Arizona, Tucson, AZ 85721
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Abstract

We use numerical methods to compute Nash equilibrium (NE) bid functions for four agents bidding in a first-price auction. Each bidder i is randomly assigned: ri [0, rmax], where 1 — ri is the Arrow-Pratt measure of constant relative risk aversion. Each ri is independently drawn from the cumulative distribution function Φ(·), a beta distribution on [0, rmax]. For various values of the maximum propensity to seek risk, rmax, the expected value of any bidder's risk characteristic, E(ri), and the probability that any bidder is risk seeking, P (ri > 1), we determine the nonlinear characteristics of the (NE) bid functions.

Keywords

auctionsequilibrium biddingnumerical analysis

JEL classification

D44: Auctions
Type
Research Article
Information
Experimental Economics , Volume 1 , Issue 2 , September 1998 , pp. 147 - 159
Copyright
Copyright © 1998 Economic Science Association

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