On Maximum Weighted Nash Welfare for Binary Valuations

TL;DR

This paper studies the maximum weighted Nash welfare rule for allocating indivisible goods among agents with binary valuations, demonstrating its desirable properties and efficient implementation.

Contribution

It proves that a specific version of MWNW is resource- and population-monotone, group-strategyproof, and polynomial-time computable for binary valuations.

Findings

MWNW is resource- and population-monotone

MWNW satisfies group-strategyproofness

MWNW can be computed in polynomial time

Abstract

We consider the problem of fairly allocating indivisible goods to agents with weights representing their entitlements. A natural rule in this setting is the maximum weighted Nash welfare (MWNW) rule, which selects an allocation maximizing the weighted product of the agents' utilities. We show that when agents have binary valuations, a specific version of MWNW is resource- and population-monotone, satisfies group-strategyproofness, and can be implemented in polynomial time.