A Truthful Mechanism for the Generalized Assignment Problem

TL;DR

This paper introduces a truthful-in-expectation mechanism for the strategic generalized assignment problem, achieving a near-optimal approximation ratio with improved simplicity and runtime over previous methods.

Contribution

It presents a novel convex optimization-based mechanism and a fractional local search algorithm for efficient, approximately truthful solutions in strategic GAP.

Findings

Achieves a $(1-1/e)$-approximation ratio for strategic GAP.

Provides a polynomial-time implementation with an efficient fractional local search.

Improves upon existing algorithms in simplicity, runtime, and approximation quality.

Abstract

We propose a truthful-in-expectation, $(1-1/e)$-approximation mechanism for a strategic variant of the generalized assignment problem (GAP). In GAP, a set of items has to be optimally assigned to a set of bins without exceeding the capacity of any singular bin. In the strategic variant of the problem we study, values for assigning items to bins are the private information of bidders and the mechanism should provide bidders with incentives to truthfully report their values. The approximation ratio of the mechanism is a significant improvement over the approximation ratio of the existing truthful mechanism for GAP. The proposed mechanism comprises a novel convex optimization program as the allocation rule as well as an appropriate payment rule. To implement the convex program in polynomial time, we propose a fractional local search algorithm which approximates the optimal solution within an arbitrarily small error leading to an approximately truthful-in-expectation mechanism. The presented algorithm improves upon the existing optimization algorithms for GAP in terms of simplicity and runtime while the approximation ratio closely matches the best approximation ratio given for GAP when all inputs are publicly known.