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Externalities and Fairness

Published: 13 May 2019 Publication History

Abstract

One of the important yet insufficiently studied subjects in fair allocation is the externality effect among agents. For a resource allocation problem, externalities imply that the share allocated to an agent may affect the utilities of other agents.
In this paper, we conduct a study of fair allocation of indivisible goods when the externalities are not negligible. Inspired by the models in the context of network diffusion, we present a simple and natural model, namely network externalities, to capture the externalities. To evaluate fairness in the network externalities model, we generalize the idea behind the notion of maximin-share () to achieve a new criterion, namely, extended-maximin-share (). Next, we consider two problems concerning our model.
First, we discuss the computational aspects of finding the value of for every agent. For this, we introduce a generalized form of partitioning problem that includes many famous partitioning problems such as maximin, minimax, and leximin. We further show that a 1/2-approximation algorithm exists for this partitioning problem.
Next, we investigate on finding approximately optimal allocations, i.e., allocations that guarantee each agent a utility of at least a fraction of his extended-maximin-share. We show that under a natural assumption that the agents are a-self-reliant, an a/2- allocation always exists. The combination of this with the former result yields a polynomial-time a/4- allocation algorithm.

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Cited By

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  • (2022)Fair Allocation with Special ExternalitiesPRICAI 2022: Trends in Artificial Intelligence10.1007/978-3-031-20862-1_1(3-16)Online publication date: 10-Nov-2022
  • (2021)Fair Allocation of Indivisible GoodsMathematics of Operations Research10.1287/moor.2020.109646:3(1038-1053)Online publication date: 1-Aug-2021

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cover image ACM Other conferences
WWW '19: The World Wide Web Conference
May 2019
3620 pages
ISBN:9781450366748
DOI:10.1145/3308558
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 13 May 2019

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Author Tags

  1. Fairness
  2. approximation
  3. externalities
  4. maximin-share
  5. networks

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WWW '19
WWW '19: The Web Conference
May 13 - 17, 2019
CA, San Francisco, USA

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Cited By

View all
  • (2022)Fair Allocation with Special ExternalitiesPRICAI 2022: Trends in Artificial Intelligence10.1007/978-3-031-20862-1_1(3-16)Online publication date: 10-Nov-2022
  • (2021)Fair Allocation of Indivisible GoodsMathematics of Operations Research10.1287/moor.2020.109646:3(1038-1053)Online publication date: 1-Aug-2021

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