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

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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.

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Authors and Affiliations

  1. Department of Economics and Finance, University of Mississippi, USA

    Mark V. Van Boening

  2. Economic Science Laboratory, 116 McClelland Hall, University of Arizona, Tucson, AZ, 85721

    Stephen J. Rassenti & Vernon L. Smith

Authors
  1. Mark V. Van Boening
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  2. Stephen J. Rassenti
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  3. Vernon L. Smith
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Van Boening, M.V., Rassenti, S.J. & Smith, V.L. Numerical Computation of Equilibrium Bid Functions in a First-Price Auction with Heterogeneous Risk Attitudes. Experimental Economics 1, 147–159 (1998). https://doi.org/10.1023/A:1009992209358

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  • DOI: https://doi.org/10.1023/A:1009992209358

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