One Dollar Each Eliminates Envy
Johannes Brustle, Jack Dippel, Vishnu V. Narayan, Mashbat, Suzuki, Adrian Vetta

TL;DR
This paper proves that a small, fixed subsidy per agent guarantees envy-free allocations in fair division problems with indivisible goods, improving previous bounds and extending results to more general valuation functions.
Contribution
It confirms that a subsidy of at most one dollar per agent suffices for additive valuations and establishes a bound of 2(n-1) dollars for general monotonic valuations, advancing fair division theory.
Findings
A subsidy of at most one dollar per agent guarantees envy-freeness for additive valuations.
For general monotonic valuations, a subsidy of at most 2(n-1) dollars per agent suffices.
The total subsidy needed for monotonic valuations does not depend on the number of items.
Abstract
We study the fair division of a collection of indivisible goods amongst a set of agents. Whilst envy-free allocations typically do not exist in the indivisible goods setting, envy-freeness can be achieved if some amount of a divisible good (money) is introduced. Specifically, Halpern and Shah (SAGT 2019, pp.374-389) showed that, given additive valuation functions where the marginal value of each item is at most one dollar for each agent, there always exists an envy-free allocation requiring a subsidy of at most dollars. The authors also conjectured that a subsidy of dollars is sufficient for additive valuations. We prove this conjecture. In fact, a subsidy of at most one dollar per agent is sufficient to guarantee the existence of an envy-free allocation. Further, we prove that for general monotonic valuation functions an envy-free allocation always exists…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
