Bid shading and risk aversion in multi-unit auctions with many bidders

We extend the analysis of optimal price taking bidding in multi-unit auctions to allow for risk aversion and a continuous random stop-out price. We show that in a discriminatory auction risk averse bidders should bid less aggressively than risk neutral bidders. However, bid shading is optimal at each price, which implies, with complete certainty, inefficient trade. This is in sharp contrast to competitive auctions where truthful bidding is optimal even under risk aversion.