One Dollar Each Eliminates Envy

by   Johannes Brustle, et al.

We study the fair division of a collection of m indivisible goods amongst a set of n 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 (n-1)· m dollars. The authors also conjectured that a subsidy of n-1 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 with a subsidy of at most 2(n-1) dollars per agent. In particular, the total subsidy required for monotonic valuations is independent of the number of items.



There are no comments yet.


page 1

page 2

page 3

page 4


Existence of EFX for Two Additive Valuations

Fair division of indivisible items is a well-studied topic in Economics ...

Achieving Envy-Freeness with Limited Subsidies under Dichotomous Valuations

We study the problem of allocating indivisible goods among agents in a f...

Achieving Envy-freeness and Equitability with Monetary Transfers

When allocating indivisible resources or tasks, an envy-free allocation ...

Fairly Allocating Many Goods with Few Queries

We investigate the query complexity of the fair allocation of indivisibl...

An EF2X Allocation Protocol for Restricted Additive Valuations

We study the problem of fairly allocating a set of m indivisible goods t...

Almost Envy-Free Allocations with Connected Bundles

We study the existence of allocations of indivisible goods that are envy...

(Almost Full) EFX Exists for Four Agents (and Beyond)

The existence of EFX allocations is a major open problem in fair divisio...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.