Single Parameter Combinatorial Auctions with Partially Public Valuations

TL;DR

This paper introduces a truthful auction mechanism for combinatorial auctions with valuations that have a public component and a private single parameter, improving approximation guarantees.

Contribution

It presents a general technique using maximal-in-range mechanisms to convert non-truthful algorithms into truthful mechanisms with better approximation ratios.

Findings

Achieves an (rac{ ext{approximation}}{ ext{logarithm of number of bidders}}) approximation in polynomial time.

Provides a ( ext{approximation}) approximation in quasi-polynomial time.

Applicable to ad-slot valuation scenarios in broadcast media.

Abstract

We consider the problem of designing truthful auctions, when the bidders' valuations have a public and a private component. In particular, we consider combinatorial auctions where the valuation of an agent $i$ for a set $S$ of items can be expressed as $v_if(S)$, where $v_i$ is a private single parameter of the agent, and the function $f$ is publicly known. Our motivation behind studying this problem is two-fold: (a) Such valuation functions arise naturally in the case of ad-slots in broadcast media such as Television and Radio. For an ad shown in a set $S$ of ad-slots, $f(S)$ is, say, the number of {\em unique} viewers reached by the ad, and $v_i$ is the valuation per-unique-viewer. (b) From a theoretical point of view, this factorization of the valuation function simplifies the bidding language, and renders the combinatorial auction more amenable to better approximation factors. We present a general technique, based on maximal-in-range mechanisms, that converts any $\alpha$-approximation non-truthful algorithm ($\alpha \leq 1$) for this problem into $\Omega(\frac{\alpha}{\log{n}})$ and $\Omega(\alpha)$-approximate truthful mechanisms which run in polynomial time and quasi-polynomial time, respectively.