Barman, S and Bhaskar, U and Pandit, Y and Pyne, S (2024) Nearly Equitable Allocations beyond Additivity and Monotonicity. In: 38th AAAI Conference on Artificial Intelligence, AAAI 2024, 20 February 2024through 27 February 2024, Vancouver, pp. 9494-9501.
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Abstract
Equitability (EQ) in fair division requires that items be allocated such that all agents value the bundle they receive equally. With indivisible items, an equitable allocation may not exist, and hence we instead consider a meaningful analog, EQx, that requires equitability up to any item. EQx allocations exist for monotone, additive valuations. However, if (1) the agents' valuations are not additive or (2) the set of indivisible items includes both goods and chores (positively and negatively valued items), then prior to the current work it was not known whether EQx allocations exist or not. We study both the existence and efficient computation of EQx allocations. (1) For monotone valuations (not necessarily additive), we show that EQx allocations always exist. Also, for the large class of weakly well-layered valuations, EQx allocations can be found in polynomial time. Further, we prove that approximately EQx allocations can be computed efficiently under general monotone valuations. (2) For non-monotone valuations, we show that an EQx allocation may not exist, even for two agents with additive valuations. Under some special cases, however, we show existence and efficient computability of EQx allocations. This includes the case of two agents with additive valuations where each item is either a good or a chore, and there are no mixed items. Copyright © 2024, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
| Item Type: | Conference Paper |
|---|---|
| Publication: | Proceedings of the AAAI Conference on Artificial Intelligence |
| Publisher: | Association for the Advancement of Artificial Intelligence |
| Additional Information: | The copyright for this article belongs to authors. |
| Keywords: | Artificial intelligence; Polynomial approximation, 'current; Additivity; Efficient computation; Fair divisions; Monotonicity; Polynomial-time; Two agents, Additives |
| Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |
| Date Deposited: | 11 Jul 2024 08:23 |
| Last Modified: | 11 Jul 2024 08:23 |
| URI: | http://eprints.iisc.ac.in/id/eprint/84816 |
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