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

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  • 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

Suggested Citation

  • Mark Van Boening & Stephen Rassenti & Vernon Smith, 1998. "Numerical Computation of Equilibrium Bid Functions in a First-Price Auction with Heterogeneous Risk Attitudes," Experimental Economics, Springer;Economic Science Association, vol. 1(2), pages 147-159, September.
    • Handle: RePEc:kap:expeco:v:1:y:1998:i:2:p:147-159
    DOI: 10.1023/A:1009992209358
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    References listed on IDEAS

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    1. 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 237-245, April.
    2. 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.
    3. Friedman, Daniel, 1992. "Theory and Misbehavior of First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1374-1378, December.
    4. Merlo, Antonio & Schotter, Andrew, 1992. "Theory and Misbehavior of First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1413-1425, December.
    5. 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 1379-1391, December.
    6. 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.
    7. 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 1392-1412, December.
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    Cited by:

    1. Paul Pezanis-Christou & Abdolkarim Sadrieh, 2003. "Elicited bid functions in (a)symmetric first-price auctions," Working Papers 85, Barcelona School of Economics.
    2. Theodore L. Turocy & Elizabeth Watson, 2012. "Reservation Values and Regret in Laboratory First‐Price Auctions: Context and Bidding Behavior," Southern Economic Journal, John Wiley & Sons, vol. 78(4), pages 1163-1180, April.
    3. 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.
    4. 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.
    5. Robert Dorsey & Laura Razzolini, 2003. "Explaining Overbidding in First Price Auctions Using Controlled Lotteries," Experimental Economics, Springer;Economic Science Association, vol. 6(2), pages 123-140, October.
    6. Paul Pezanis-Christou & Andres Romeu, 2016. "Structural Analysis of First-Price Auction Data: Insights from the Laboratory," School of Economics and Public Policy Working Papers 2016-17, University of Adelaide, School of Economics and Public Policy.
    7. 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.

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