Barman, S and Kar, D and Pathak, S (2024) Parameterized Guarantees for Almost Envy-Free Allocations. In: AAMAS 2024, 6 May 2024through 10 May 2024, Auckland, New Zealand, pp. 151-159.
Full text not available from this repository.Abstract
We study fair allocation of indivisible goods among agents with additive valuations. We obtain novel approximation guarantees for two of the strongest fairness notions in discrete fair division, namely envy-free up to the removal of any positively-valued good (EFx) and pairwise maximin shares (PMMS). Our approximation guarantees are in terms of an instance-dependent parameter γ � (0, 1] that upper bounds, for each indivisible good in the given instance, the multiplicative range of nonzero values for the good across the agents. First, we consider allocations wherein, between any pair of agents and up to the removal of any positively-valued good, the envy is multiplicatively bounded. Specifically, the current work develops a polynomial-time algorithm that computes a (Equation presented)-approximately EFx allocation for any given fair division instance with range parameter γ � (0, 1]. For instances with γ � 0.511, the obtained approximation guarantee for EFx surpasses the previously best-known approximation bound of (��1) � 0.618, here � denotes the golden ratio. Furthermore, we study multiplicative approximations for PMMS. For fair division instances with range parameter γ � (0, 1], the current paper develops a polynomial-time algorithm for finding allocations wherein the PMMS requirement is satisfied, between every pair of agents, within a multiplicative factor of 56γ. En route to this result, we obtain novel existential and computational guarantees for 56 -approximately PMMS allocations under restricted additive valuations. © 2024 International Foundation for Autonomous Agents and Multiagent Systems.
| Item Type: | Conference Paper |
|---|---|
| Publication: | Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS |
| Publisher: | International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS) |
| Additional Information: | The copyright for this article belongs to International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS). |
| Keywords: | Autonomous agents; Multi agent systems; Parameter estimation; Parameterization; Polynomial approximation, 'current; Discrete fair division; Envy free; Envy-freeness up to any good (EFx); Fair divisions; Indivisible good; Maximin; Pairwise maximin share; Polynomial-time algorithms; Restricted additive valuation, Additives |
| Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |
| Date Deposited: | 31 Jul 2024 04:59 |
| Last Modified: | 31 Jul 2024 04:59 |
| URI: | http://eprints.iisc.ac.in/id/eprint/85658 |
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