On approximating optimal auctions

We study the following problem: A seller wishes to sell an item to a group of self-interested agents. Each agent i has a privately known valuation vi for the object. Given a distribution on these valuations, our goal is to construct an auction that maximizes the seller's expected revenue (optimal auction). The auction must be incentive compatible and satisfy individual rationality. We present a simple generic auction that guarantees at least half of the optimal revenue. We generalize this result in several directions, in particular, for the case of multiple copies with unit demand. Our auction requires the ability to learn (or compute) in polynomial time the conditional distribution of the agent with the maximal valuation, given the valuations of the other agents. We show that this ability is in some sense essential. Finally we suggest a generalization of our auction and argue that it will generate a revenue which is close to optimal for reasonable distributions. In particular we show this under an independence assumption

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