  The existing literature on optimal auctions focuses on optimizing the
expected revenue of the seller, and is appropriate for risk-neutral sellers. In
this paper, we identify good mechanisms for risk-averse sellers. As is standard
in the economics literature, we model the risk-aversion of a seller by endowing
the seller with a monotone concave utility function. We then seek robust
mechanisms that are approximately optimal for all sellers, no matter what their
levels of risk-aversion are. We have two main results for multi-unit auctions
with unit-demand bidders whose valuations are drawn i.i.d. from a regular
distribution. First, we identify a posted-price mechanism called the Hedge
mechanism, which gives a universal constant factor approximation; we also show
for the unlimited supply case that this mechanism is in a sense the best
possible. Second, we show that the VCG mechanism gives a universal constant
factor approximation when the number of bidders is even only a small multiple
of the number of items. Along the way we point out that Myerson's
characterization of the optimal mechanisms fails to extend to
utility-maximization for risk-averse sellers, and establish interesting
properties of regular distributions and monotone hazard rate distributions.
