Simple Mechanisms for Subadditive Buyers via Duality

TL;DR

This paper introduces simple, approximately revenue-optimal mechanisms for multi-item auctions with subadditive buyers, extending duality frameworks and achieving constant or logarithmic approximation factors.

Contribution

It unifies and improves previous results by applying duality to derive simple mechanisms that approximate optimal revenue for subadditive valuations.

Findings

Sequential posted price mechanism achieves constant approximation for XOS valuations.

Approximation factor degrades to O(log m) for subadditive valuations.

Extended duality framework provides effective revenue benchmarks.

Abstract

We provide simple and approximately revenue-optimal mechanisms in the multi-item multi-bidder settings. We unify and improve all previous results, as well as generalize the results to broader cases. In particular, we prove that the better of the following two simple, deterministic and Dominant Strategy Incentive Compatible mechanisms, a sequential posted price mechanism or an anonymous sequential posted price mechanism with entry fee, achieves a constant fraction of the optimal revenue among all randomized, Bayesian Incentive Compatible mechanisms, when buyers' valuations are XOS over independent items. If the buyers' valuations are subadditive over independent items, the approximation factor degrades to $O(\log m)$, where $m$ is the number of items. We obtain our results by first extending the Cai-Devanur-Weinberg duality framework to derive an effective benchmark of the optimal revenue for subadditive bidders, and then analyzing this upper bound with new techniques.