The Complexity of Fair Division of Indivisible Items with Externalities

by   Argyrios Deligkas, et al.

We study the computational complexity of fairly allocating a set of indivisible items under externalities. In this recently-proposed setting, in addition to the utility the agent gets from their bundle, they also receive utility from items allocated to other agents. We focus on the extended definitions of envy-freeness up to one item (EF1) and of envy-freeness up to any item (EFX), and we provide the landscape of their complexity for several different scenarios. We prove that it is NP-complete to decide whether there exists an EFX allocation, even when there are only three agents, or even when there are only six different values for the items. We complement these negative results by showing that when both the number of agents and the number of different values for items are bounded by a parameter the problem becomes fixed-parameter tractable. Furthermore, we prove that two-valued and binary-valued instances are equivalent and that EFX and EF1 allocations coincide for this class of instances. Finally, motivated from real-life scenarios, we focus on a class of structured valuation functions, which we term agent/item-correlated. We prove their equivalence to the “standard” setting without externalities. Therefore, all previous results for EF1 and EFX apply immediately for these valuations.


page 1

page 2

page 3

page 4


Fair allocation of combinations of indivisible goods and chores

We consider the problem of fairly dividing a set of items. Much of the f...

High-Multiplicity Fair Allocation Using Parametric Integer Linear Programming

Using insights from parametric integer linear programming, we significan...

Seasonal Goods and Spoiled Milk: Pricing for a Limited Shelf-Life

We examine the case of items with a limited shelf-life where storing an ...

Mechanisms for Trading Durable Goods

We consider trading indivisible and easily transferable durable goods, w...

Jealousy-freeness and other common properties in Fair Division of Mixed Manna

We consider a fair division setting where indivisible items are allocate...

The Good, the Bad and the Submodular: Fairly Allocating Mixed Manna Under Order-Neutral Submodular Preferences

We study the problem of fairly allocating indivisible goods (positively ...

Safe Disassociation of Set-Valued Datasets

Disassociation introduced by Terrovitis et al. is a bucketization based ...

Please sign up or login with your details

Forgot password? Click here to reset