Approximating Optimal Auctions

We study a fundamental problem in micro economics called optimal auction design: A seller wishes to sell an item to a group of self-interested agents. Each agent i has a privately known value for winning the object. Given a joint distribution of these values, the goal is to construct an optimal auction, i.e. a truth revealing protocol that maximizes the seller’s expected revenue. We introduce a novel generic method for the construction of near-optimal auctions that satisfy ex-post individual rationality. Our method guarantees an expected revenue of at least 1/2 of the optimum for any given distribution of the values of the agents. Moreover, we show that unless the agents’ values are strongly dependent, the expected revenue of our auctions is almost optimal. Our auctions run in polynomial time. For general distributions of the agents’ values, we show that no deterministic polynomial time ascending auction can achieve an approximation ratio better than 7/8. The design of practical auctions may give rise to limitations on the designer of the auction which are not reflected in classic economic models. We study two such limitations and show tight bounds on the approximation ratio that can be obtained by any polynomial-time auction under each of these limitations. Classification codes: 68Q25, 91B26