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We investigate approximately optimal mechanisms in settings where bidders'utility functions are non-linear; specifically, convex, with respect topayments (such settings arise, for instance, in procurement auctions forenergy). We provide constant factor approximation guarantees for mechanismsthat are independent of bidders' private information (i.e., prior-free), andfor mechanisms that rely to an increasing extent on that information (i.e.,detail free). We also describe experiments, which show that for randomly drawnmonotone hazard rate distributions, our mechanisms achieve at least 80\% of theoptimal revenue, on average. Both our theoretical and experimental results showthat in the convex payment setting, it is desirable to allocate across multiplebidders, rather than only to bidders with the highest (virtual) value, as inthe traditional quasi-linear utility setting.

Simple vs Optimal Mechanisms in Auctions with Convex Payments