Combinatorial Auctions via Posted Prices

TL;DR

This paper demonstrates that simple posted price mechanisms can guarantee at least half of the optimal welfare in Bayesian combinatorial auctions with subadditive valuations, providing a constructive, polynomial-time approach.

Contribution

It introduces a constructive method to compute posted prices that achieve a 50% welfare approximation for subadditive valuations, including submodular functions, in polynomial time.

Findings

Guarantee of at least half the optimal welfare with posted prices

First polynomial-time constant-factor DSIC mechanism for Bayesian submodular auctions

Extension of results to valuations with complements, with linear degradation

Abstract

We study anonymous posted price mechanisms for combinatorial auctions in a Bayesian framework. In a posted price mechanism, item prices are posted, then the consumers approach the seller sequentially in an arbitrary order, each purchasing her favorite bundle from among the unsold items at the posted prices. These mechanisms are simple, transparent and trivially dominant strategy incentive compatible (DSIC). We show that when agent preferences are fractionally subadditive (which includes all submodular functions), there always exist prices that, in expectation, obtain at least half of the optimal welfare. Our result is constructive: given black-box access to a combinatorial auction algorithm A, sample access to the prior distribution, and appropriate query access to the sampled valuations, one can compute, in polytime, prices that guarantee at least half of the expected welfare of A. As a corollary, we obtain the first polytime (in n and m) constant-factor DSIC mechanism for Bayesian submodular combinatorial auctions, given access to demand query oracles. Our results also extend to valuations with complements, where the approximation factor degrades linearly with the level of complementarity.