  We study simple and approximately optimal auctions for agents with a
particular form of risk-averse preferences. We show that, for symmetric agents,
the optimal revenue (given a prior distribution over the agent preferences) can
be approximated by the first-price auction (which is prior independent), and,
for asymmetric agents, the optimal revenue can be approximated by an auction
with simple form. These results are based on two technical methods. The first
is for upper-bounding the revenue from a risk-averse agent. The second gives a
payment identity for mechanisms with pay-your-bid semantics.
