Truthful Mechanisms via Greedy Iterative Packing

TL;DR

This paper introduces loser-independence, a property of approximation algorithms, enabling their use in truthful mechanisms through a greedy iterative packing approach, applicable to various optimization problems in algorithmic game theory.

Contribution

It identifies loser-independence as a key property that allows approximation algorithms to be used in truthful mechanisms, expanding their applicability.

Findings

Loser-independent algorithms do not change outcomes when losing bids increase unless they become winners.

The framework yields truthful mechanisms for problems involving submodular function maximization under constraints.

Applicable to online mechanism design scenarios.

Abstract

An important research thread in algorithmic game theory studies the design of efficient truthful mechanisms that approximate the optimal social welfare. A fundamental question is whether an \alpha-approximation algorithm translates into an \alpha-approximate truthful mechanism. It is well-known that plugging an \alpha-approximation algorithm into the VCG technique may not yield a truthful mechanism. Thus, it is natural to investigate properties of approximation algorithms that enable their use in truthful mechanisms. The main contribution of this paper is to identify a useful and natural property of approximation algorithms, which we call loser-independence; this property is applicable in the single-minded and single-parameter settings. Intuitively, a loser-independent algorithm does not change its outcome when the bid of a losing agent increases, unless that agent becomes a winner. We demonstrate that loser-independent algorithms can be employed as sub-procedures in a greedy iterative packing approach while preserving monotonicity. A greedy iterative approach provides a good approximation in the context of maximizing a non-decreasing submodular function subject to independence constraints. Our framework gives rise to truthful approximation mechanisms for various problems. Notably, some problems arise in online mechanism design.