Hostname: page-component-7b9c58cd5d-v2ckm Total loading time: 0 Render date: 2025-03-17T05:34:40.995Z Has data issue: false hasContentIssue false

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
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

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.

JEL classification

Type
Research Article
Copyright
Copyright © 1998 Economic Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cox, J.C. and Oaxaca, R. (1994a). “Inducing Risk Neutral Preferences: Further Analysis of the Data.” Department of Economics, University of Arizona, Journal of Risk and Uncertainty, to appear.Google Scholar
Cox, J.C. and Oaxaca, R. (1994b). “Is Bidding Behavior Consistent with Bidding Theory for Private Value Auctions.” Department of Economics, University of Arizona, In Isaac, R.M. (ed.), Research in Experimental Economics, Vol. 6, to appear.Google Scholar
Cox, J.C., Roberson, B., and Smith, V.L. (1982a). “Theory and Behavior of Single Object Auctions.” In Smith, Vernon L. (ed.), Research in Experimental Economics, vol. 2. Greenwich, CT: JAI Press.Google Scholar
Cox, J.C., Smith, V.L., and Walker, J.M. (1982b). “Auction Market Theory of Heterogeneous Bidders.” Economic Letters. 9, 319325.CrossRefGoogle Scholar
Cox, J.C., Smith, V.L., and Walker, J.M. (1988). “Theory and Individual Behavior in First-Price Auctions.” Journal of Risk and Uncertainty. 1, 6169.CrossRefGoogle Scholar
Cox, J.C., Smith, V.L., and Walker, J.M. (1992). “Theory and Misbehavior of First-Price Auctions: Comment.” American Economic Review. 82, 13921412.Google Scholar
Law, A.M. and Kelton, W.D. (1991). Simulation Modeling and Analysis, 2nd ed. New York: McGraw-Hill.Google Scholar
Pearson, K. (ed.). (1934). Tables of the Incomplete Beta-Function. Cambridge: Cambridge University Press.Google Scholar
Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. (1986). Numerical Recipes, Cambridge: Cambridge University Press.Google Scholar
Smith, V.L. and Walker, J.M. (1992). “Rewards, Experience and Decision Costs in First Price Auctions.” Economic Inquiry, to appear.Google Scholar
Yakowitz, S. and Szidarovszky, F. (1989). An Introduction to Numerical Computations. New York: MacMillan Publishing Co.Google Scholar