The Complexity of Fair Division of Indivisible Items with Externalities

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F24%3A00369990" target="_blank" >RIV/68407700:21240/24:00369990 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1609/aaai.v38i9.28822" target="_blank" >https://doi.org/10.1609/aaai.v38i9.28822</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1609/aaai.v38i9.28822" target="_blank" >10.1609/aaai.v38i9.28822</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Complexity of Fair Division of Indivisible Items with Externalities

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The Complexity of Fair Division of Indivisible Items with Externalities

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/EH22_008%2F0004590" target="_blank" >EH22_008/0004590: Robotika a pokročilá průmyslová výroba</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the 38th AAAI Conference on Artificial Intelligence

ISBN

—

ISSN

2159-5399

e-ISSN

2374-3468

Počet stran výsledku

9

Strana od-do

9653-9661

Název nakladatele

AAAI Press

Místo vydání

Menlo Park

Místo konání akce

Vancouver

Datum konání akce

20. 2. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001241512400025