Bayesian Auctions with Efficient Queries

TL;DR

This paper studies the query complexity in Bayesian auction mechanisms, showing that limited distribution access can still yield near-optimal revenue in certain auction settings, challenging the assumption of perfect distribution knowledge.

Contribution

It introduces the first analysis of query complexity in Bayesian mechanisms, providing tight bounds and efficient schemes for various auction types.

Findings

Logarithmic lower bounds on query complexity for constant revenue approximation

Efficient query schemes for single-item and multi-item auctions with limited distribution access

No need for regularity or monotone hazard rate assumptions in auction design

Abstract

Generating good revenue is one of the most important problems in Bayesian auction design, and many (approximately) optimal dominant-strategy incentive compatible (DSIC) Bayesian mechanisms have been constructed for various auction settings. However, most existing studies do not consider the complexity for the seller to carry out the mechanism. It is assumed that the seller knows "each single bit" of the distributions and is able to optimize perfectly based on the entire distributions. Unfortunately, this is a strong assumption and may not hold in reality: for example, when the value distributions have exponentially large supports or do not have succinct representations. In this work we consider, for the first time, the query complexity of Bayesian mechanisms. We only allow the seller to have limited oracle accesses to the players' value distributions, via quantile queries and value queries. For a large class of auction settings, we prove logarithmic lower-bounds for the query complexity for any DSIC Bayesian mechanism to be of any constant approximation to the optimal revenue. For single-item auctions and multi-item auctions with unit-demand or additive valuation functions, we prove tight upper-bounds via efficient query schemes, without requiring the distributions to be regular or have monotone hazard rate. Thus, in those auction settings the seller needs to access much less than the full distributions in order to achieve approximately optimal revenue.