Abstract
We use numerical methods to compute Nash equilibrium (NE) bid functions for four agents bidding in a first-price auction. Each bidderi is randomly assigned:r i ∈ [0,r max], where 1 −r i is the Arrow-Pratt measure of constant relative risk aversion. Eachr i is independently drawn from the cumulative distribution function Ф(·), a beta distribution on [0,r max]. For various values of the maximum propensity to seek risk,r max, the expected value of any bidder's risk characteristic,E (r i ), and the probability that any bidder is risk seeking,P (r i > 1), we determine the nonlinear characteristics of the (NE) bid functions.
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