Optimal auctions with correlated bidders are easy

Shahar Dobzinski, Hu Fu, Robert D. Kleinberg
2011 Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11  
We consider the problem of designing a revenue-maximizing auction for a single item, when the values of the bidders are drawn from a correlated distribution. We observe that there exists an algorithm that finds the optimal randomized mechanism that runs in time polynomial in the size of the support. We leverage this result to show that in the oracle model introduced by Ronen and Saberi [FOCS'02], there exists a polynomial time truthful in expectation mechanism that provides a (1.5 +
more » ... ion to the revenue achievable by an optimal truthful-inexpectation mechanism, and a polynomial time deterministic truthful mechanism that guarantees 5 3 approximation to the revenue achievable by an optimal deterministic truthful mechanism. We show that the 5 3 -approximation mechanism provides the same approximation ratio also with respect to the optimal truthful-in-expectation mechanism. This shows that the performance gap between truthful-in-expectation and deterministic mechanisms is relatively small. En route, we solve an open question of Mehta and Vazirani [EC'04]. Finally, we extend some of our results to the multi-item case, and show how to compute the optimal truthful-in-expectation mechanisms for bidders with more complex valuations. 1 For example, even if a bidder is risk neutral, she may not have a budget to cover a payment many times her bid.
doi:10.1145/1993636.1993655 dblp:conf/stoc/DobzinskiFK11 fatcat:ixf35q2aijhqvft3wyd7mnvq3m