Derandomization of auctions

Abstract

We study the role of randomization in seller optimal (i.e., profit maximization) auctions. Bayesian optimal auctions (e.g., Myerson, 1981) assume that the valuations of the agents are random draws from a distribution and prior-free optimal auctions either are randomized (e.g., Goldberg et al., 2006) or assume the valuations are randomized (e.g., Segal, 2003). Is randomization fundamental to profit maximization in auctions? Our main result is a general approach to derandomize single-item multi-unit unit-demand auctions while approximately preserving their performance (i.e., revenue). Our general technique is constructive but not computationally tractable. We complement the general result with the explicit and computationally-simple derandomization of a particular auction. Our results are obtained through analogy to hat puzzles that are interesting in their own right.

Hats, auctions and derandomization

“…Therefore, the competitive ratio of DOP is unbounded. Similar examples regarding the performances of DOP in the bi‐valued auction setting appeared already in Goldberg et al , and in Aggarwal et al .…”

“…It is well known (see for example ) that in order to achieve truthfulness one can use only the set of bid independent auctions , i.e., auctions in which the computation of the price offered to a bidder is done while ignoring its own bid value. Hence, an intuitive auction that often comes to one's mind is the Deterministic Optimal Price ( DOP ) auction . In this auction the mechanism computes and offers each bidder the price of an optimal offline auction for all other bids.…”

“…Aggarwal et al later showed how to construct from any randomized auction a deterministic, asymmetric auction with approximately the same revenue. In order to establish the result the authors used guessing auctions , in which the bidder gets the good only if the price equals exactly the bid (rather than lower or equal, as in a the standard setting).…”

“…That is, there exists an auction with no multiplicative loss and with only additive loss, and every auction has at‐least these losses. Let us note here, that if we restrict ourselves to anonymous auctions (symmetric) then we have a multiplicative loss of and an additive loss of over the revenue of the best offline .…”

Core-competitive Auctions

“…Formally, we show that no mechanism that is anonymous and satisfies independence of irrelevant alternatives can provide an approximation ratio better then O( ln(k)). A word of caution: while anonymity and independence of irrelevant alternatives are commonly used assumptions in lower bounds for deterministic mechanisms [Ashlagi et al 2012], they are not completely innocuous as shown by [Aggarwal et al 2011]. …”