First-Price Auctions with Risk-Averse Bidders

We consider first-price auctions with asymmetric independent private values and risk-averse bidders. We show that a bidder´s expected equilibrium equilibrium bid strategy satisfies that her utility identically equal to her accumulated expected marginal utility. For symmetric first-price auctions with weakly risk-averse bidders, we give the explicit approximation expression of the equilibrium bid strategies by a perturbation method, by which we figure out the seller´s expected revenue and each bidder´s expected equilibrium utility.