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

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Author Info
Mark Van Boening
Stephen Rassenti
Vernon Smith

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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 ɛ [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(ċ), 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. Copyright Kluwer Academic Publishers 1998

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Publisher Info
Article provided by Springer in its journal Experimental Economics.

Volume (Year): 1 (1998)
Issue (Month): 2 (September)
Pages: 147-159
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Handle: RePEc:kap:expeco:v:1:y:1998:i:2:p:147-159

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Related research
Keywords: auctions; equilibrium bidding; numerical analysis;

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Smith, Vernon L & Walker, James M, 1993. "Rewards, Experience and Decision Costs in First Price Auctions," Economic Inquiry, Oxford University Press, vol. 31(2), pages 237-45, April.
  2. Cox, James C & Smith, Vernon L & Walker, James M, 1992. "Theory and Misbehavior of First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1392-412, December. [Downloadable!] (restricted)
  3. Friedman, Daniel, 1992. "Theory and Misbehavior of First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1374-78, December. [Downloadable!] (restricted)
  4. Cox, James C & Smith, Vernon L & Walker, James M, 1988. " Theory and Individual Behavior of First-Price Auctions," Journal of Risk and Uncertainty, Springer, vol. 1(1), pages 61-99, March.
  5. Cox, James C. & Smith, Vernon L. & Walker, James M., 1982. "Auction market theory of heterogeneous bidders," Economics Letters, Elsevier, vol. 9(4), pages 319-325. [Downloadable!] (restricted)
  6. Merlo, Antonio & Schotter, Andrew, 1992. "Theory and Misbehavior of First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1413-25, December. [Downloadable!] (restricted)
  7. Kagel, John H & Roth, Alvin E, 1992. "Theory and Misbehavior in First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1379-91, December. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Sadrieh, A. & Pezanis-Christou, P., 2003. "Elicited bid functions in (a)symmetric first-price auctions," Discussion Paper 58, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  2. Tibor Neugebauer, 2007. "Bid and price effects of increased competition in the first-price auction: experimental evidence," Working Papers of CREFI-LSF (Centre of Research in Finance - Luxembourg School of Finance) 07-17, CREFI-LSF, University of Luxembourg. [Downloadable!]
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