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

Author Info

  • Mark Van Boening
  • Stephen Rassenti
  • Vernon Smith

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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File URL: http://hdl.handle.net/10.1023/A:1009992209358
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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
Contact details of provider: Web page: http://www.springerlink.com/link.asp?id=102888

Keywords: auctions; equilibrium bidding; numerical analysis;

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  1. 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.
  2. Smith, Vernon L & Walker, James M, 1993. "Rewards, Experience and Decision Costs in First Price Auctions," Economic Inquiry, Western Economic Association International, vol. 31(2), pages 237-45, April.
  3. 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.
  4. Friedman, Daniel, 1992. "Theory and Misbehavior of First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1374-78, December.
  5. 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.
  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.
  7. 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.
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Cited by:

  1. Paul Pezanis-Christou & Abdolkarim Sadrieh, 2003. "Elicited bid functions in (a)symmetric first-price auctions," UFAE and IAE Working Papers 578.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Tibor Neugebauer, 2007. "Bid and price effects of increased competition in the first-price auction: experimental evidence," LSF Research Working Paper Series 07-17, Luxembourg School of Finance, University of Luxembourg.
  3. Elizabeth Watson & Theodore L. Turocy, 2011. "Reservation values and regret in laboratory first price auctions: Context and bidding behavior," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 11-14, School of Economics, University of East Anglia, Norwich, UK..
  4. Robert Dorsey & Laura Razzolini, 2003. "Explaining Overbidding in First Price Auctions Using Controlled Lotteries," Experimental Economics, Springer, vol. 6(2), pages 123-140, October.
  5. Neugebauer, Tibor & Selten, Reinhard, 2006. "Individual behavior of first-price auctions: The importance of information feedback in computerized experimental markets," Games and Economic Behavior, Elsevier, vol. 54(1), pages 183-204, January.
  6. Gentry, Matthew & Li, Tong & Lu, Jingfeng, 2015. "Existence of monotone equilibrium in first price auctions with private risk aversion and private initial wealth," Games and Economic Behavior, Elsevier, vol. 94(C), pages 214-221.

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