A Truthful Randomized Mechanism for Combinatorial Public Projects via Convex Optimization

TL;DR

This paper presents a polynomial-time, truthful mechanism that achieves the best possible constant-factor approximation for maximizing social welfare in combinatorial public projects with submodular valuations, advancing algorithmic mechanism design.

Contribution

It introduces the first constant-factor approximation mechanism for a natural NP-hard variant of combinatorial public projects using convex optimization techniques.

Findings

Achieves a (1-1/e)-approximation ratio.

Mechanism is truthful-in-expectation.

Applicable to matroid rank sum valuations.

Abstract

In Combinatorial Public Projects, there is a set of projects that may be undertaken, and a set of self-interested players with a stake in the set of projects chosen. A public planner must choose a subset of these projects, subject to a resource constraint, with the goal of maximizing social welfare. Combinatorial Public Projects has emerged as one of the paradigmatic problems in Algorithmic Mechanism Design, a field concerned with solving fundamental resource allocation problems in the presence of both selfish behavior and the computational constraint of polynomial-time. We design a polynomial-time, truthful-in-expectation, (1-1/e)-approximation mechanism for welfare maximization in a fundamental variant of combinatorial public projects. Our results apply to combinatorial public projects when players have valuations that are matroid rank sums (MRS), which encompass most concrete examples of submodular functions studied in this context, including coverage functions, matroid weighted-rank functions, and convex combinations thereof. Our approximation factor is the best possible, assuming P != NP. Ours is the first mechanism that achieves a constant factor approximation for a natural NP-hard variant of combinatorial public projects.