A New Derandomization of Auctions

Abstract

Let A be a randomized, unlimited supply, unit demand, single-item auction, which given a bid-vector b ∈ [h]ⁿ, has expected profit ${\mathbb E}[P(b)]$. Aggarwal et al. showed that given A, there exists a deterministic auction which given a bid-vector b, guarantees a profit of ${\mathbb E}[P(b)]/4 - O(h)$. In this paper we show that given A, there exists a deterministic auction which given a bid-vector b of length n, guarantees a profit of ${\mathbb E}[P(b)]- O(h\sqrt{n \ln hn})$. As is the case with the construction of Aggarwal et al., our construction is not polynomial time computable.