On the hardness of optimal auctions

We study a fundamental problem in microeconomics 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 valuation v_i for the object. Given a distribution on these valuations, the goal is to construct an optimal auction, i.e. a truth revealing protocol that maximizes the seller´s expected revenue. We study this problem from a computational perspective and show several lower bounds. In particular we prove that no deterministic polynomial time ascending auction can achieve an approximation ratio better than 3/4. The probability distribution constructed in our example has sensitive dependencies among the agents. In contrast, we show that if the dependency between the agents´ valuations is bounded, the problem can be approximated with a factor close to 1.