Achieving Envy-Freeness with Limited Subsidies under Dichotomous Valuations

Barman, S and Krishna, A and Narahari, Y and Sadhukan, S (2022) Achieving Envy-Freeness with Limited Subsidies under Dichotomous Valuations. In: 31st International Joint Conference on Artificial Intelligence, IJCAI 2022, 23 - 29 July 2022, Vienna, pp. 60-66.

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Abstract

We study the problem of allocating indivisible goods among agents in a fair manner. While envy-free allocations of indivisible goods are not guaranteed to exist, envy-freeness can be achieved by additionally providing some subsidy to the agents. These subsidies can be alternatively viewed as a divisible good (money) that is fractionally assigned among the agents to realize an envy-free outcome. In this setup, we bound the subsidy required to attain envy-freeness among agents with dichotomous valuations, i.e., among agents whose marginal value for any good is either zero or one. We prove that, under dichotomous valuations, there exists an allocation that achieves envy-freeness with a per-agent subsidy of either 0 or 1. Furthermore, such an envy-free solution can be computed efficiently in the standard value-oracle model. Notably, our results hold for general dichotomous valuations and, in particular, do not require the (dichotomous) valuations to be additive, submodular, or even subadditive. Also, our subsidy bounds are tight and provide a linear (in the number of agents) factor improvement over the bounds known for general monotone valuations. © 2022 International Joint Conferences on Artificial Intelligence. All rights reserved.

Item Type:	Conference Paper
Publication:	IJCAI International Joint Conference on Artificial Intelligence
Publisher:	International Joint Conferences on Artificial Intelligence
Additional Information:	The copyright for this article belongs to the International Joint Conferences on Artificial Intelligence.
Keywords:	Envy free; Free allocation; Free solutions; Indivisible good; Marginal values; Oracle model; Standard values; Submodular
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	06 Oct 2022 11:02
Last Modified:	06 Oct 2022 11:02
URI:	https://eprints.iisc.ac.in/id/eprint/77251

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