Dividing Goods and Bads Under Additive Utilities

Bogomolnaia, Anna; Moulin, Hervé; Sandomirskiy, Fedor; Yanovskaya, Elena

doi:10.2139/ssrn.2860002

Cited by 14 publications

(21 citation statements)

References 2 publications

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“…Regarding fair division (see, e.g., Brams & Taylor, 1996;Bouveret, Chevaleyre, & Maudet, 2016;, while there is some work on chore division (see, e.g., Aziz, Rauchecker, Schryen, & Walsh, 2017;Bogomolnaia, Moulin, Sandomirskiy, & Yanovskaya, 2016, for recent work), not much is known about settings where an item can be seen as negative for an agent and positive for another one while a third agent does not care about receiving it; 6 still, there are many pratical contexts where this assumption is plausible, such as the allocation of papers to reviewers. If there is no constraint on the allocation, then obviously an item will be assigned to an agent who likes it, provided there is at least one such agent; but if there are constraints (such as balancedness), then it may be the case that an agent gets an item she does not want even though someone expressed a positive preference for it.…”

Section: Discussionmentioning

confidence: 99%

Hedonic Games with Ordinal Preferences and Thresholds

Kerkmann¹,

Lang²,

Rey³

et al. 2020

jair

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We propose a new representation setting for hedonic games, where each agent partitions the set of other agents into friends, enemies, and neutral agents, with friends and enemies being ranked. Under the assumption that preferences are monotonic (respectively, antimonotonic) with respect to the addition of friends (respectively, enemies), we propose a bipolar extension of the responsive extension principle, and use this principle to derive the (partial) preferences of agents over coalitions. Then, for a number of solution concepts, we characterize partitions that necessarily or possibly satisfy them, and we study the related problems in terms of their complexity.

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Section: Discussionmentioning

confidence: 99%

Hedonic Games with Ordinal Preferences and Thresholds

Kerkmann¹,

Lang²,

Rey³

et al. 2020

jair

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“…Let z be a competitive allocation Pareto inferior to the feasible allocation y. Some agent i * strictly prefers y i * to z i * which implies p • z i * < p • y i * by (1). So if we show p • z i ≤ p • y i for all i, we contradict z N = y N by summing up these inequalities.…”

Section: Proofmentioning

confidence: 94%

“…Here CR splits a between agents 1 and 2, which coalition {1, 3} blocks by giving 2 3 of a to agent 1. Remark 2: It is easy to check that CR meets Independence of Lost Bids, the translation of Maskin Monotonicity under linear preferences: see the precise definition in [1]. Just as in Proposition 2 of that paper, CR is characterized by, essentially, combining this property with Efficiency.…”

Section: Proofmentioning

confidence: 95%

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Games with Incomplete Information on One Side as Games with Incomplete Information on Both Sides and Asymmetric Computational Resources

Victoria

Gavrilovich

2016

SSRN Journal

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Dividing goods and bads under additive utilities * When utilities are additive, we uncovered in our previous paper [1] many similarities but also surprising differences in the behavior of the familiar Competitive rule (with equal incomes), when we divide (private) goods or bads. The rule picks in both cases the critical points of the product of utilities (or disutilities) on the efficiency frontier, but there is only one such point if we share goods, while there can be exponentially many in the case of bads.We extend this analysis to the fair division of mixed items: each item can be viewed by some participants as a good and by others as a bad, with corresponding positive or negative marginal utilities. We find that the division of mixed items boils down, normatively as well as computationally, to a variant of an all goods problem, or of an all bads problem: in particular the task of dividing the non disposable items must be either good news for everyone, or bad news for everyone.If at least one feasible utility profile is positive, the Competitive rule picks the unique maximum of the product of (positive) utilities. If no feasible utility profile is positive, this rule picks all critical points of the product of disutilities on the efficient frontier.

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“…The problem of effective resource allocation occurs in various applied problems [4]. If the resource value is limited and the participants interests do not coincide, a conflict situation arises.…”

Section: Introductionmentioning

confidence: 99%

About scarce resources allocation in conditions of incomplete information

Dodonova¹

2017

Collection of Selected Papers of the III International Conference on Information Technology and Nanotechnology

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The article examines the problem of the efficient allocation of resources in conditions of incomplete information concerning the parameters of agents' utility functions. Through business game the results are modeled and compared in conditions of incomplete information concerning the agents' utility functions.We experimentally prove the inexpediency of information distortion of the agents' effectiveness when using a nonmanipulative distribution mechanism in a multi-step game.

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Dividing Goods and Bads Under Additive Utilities

Cited by 14 publications

References 2 publications

Hedonic Games with Ordinal Preferences and Thresholds

Hedonic Games with Ordinal Preferences and Thresholds

Games with Incomplete Information on One Side as Games with Incomplete Information on Both Sides and Asymmetric Computational Resources

About scarce resources allocation in conditions of incomplete information

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