  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.
