Approximately optimal auctions for correlated bidders

Abstract

We consider the design of dominant strategy incentive compatible, revenue-maximizing auctions for an indivisible good, when bidders' values are drawn from a correlated distribution. For independent distributions, Myerson showed that the optimal auction for risk-neutral bidders remains incentive compatible regardless of bidders' risk attitudes. We show that, for correlated distributions, the same is true when only two bidders are involved, whereas for more bidders, randomization can generate strictly more revenue. However, for risk-neutral bidders, we show this gain is never more than a 53-factor.This is a consequence of two results of independent interest: (1) a polynomial-time derandomization of auctions for two bidders; (2) a polynomial-time computable deterministic auction that 53-approximates the optimal revenue extractable from risk-neutral bidders.Moreover, we give a polynomial-time algorithm to compute optimal auctions for a constant number of bidders, and for any number of bidders we give polynomial-time algorithms with approximation factors arbitrarily close to 32.