Equilibrium Linear Bidding Strategies

Symmetric bidding models are considered in which all bidders start with the same prior distribution on the value of the subject of the auction. In addition, each bidder is assumed to develop his own independent estimate. Each bidder's strategy must be a preselected linear function of his estimate. Closed form expressions are obtained for equilibrium sets of such strategies and the resulting expected profit to each bidder when the estimates are drawn from a Weibull distribution. These equilibrium linear strategies approach equilibrium multiplicative strategies as the estimating accuracy improves relative to the common prior information.