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Register a new userJealousy-freeness and other common properties in Fair Division of Mixed Manna
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Martin Aleksandrov D
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Authors
Martin Aleksandrov
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We consider a fair division setting where indivisible items are allocated to agents. Each agent in the setting has strictly negative, zero or strictly positive utility for each item. We, thus, make a distinction between items that are good for some agents and bad for other agents (i.e. mixed), good for everyone (i.e. goods) or bad for everyone (i.e. bads). For this model, we study axiomatic concepts of allocations such as jealousy-freeness up to one item, envy-freeness up to one item and Pareto-optimality. We obtain many new possibility and impossibility results in regard to combinations of these properties. We also investigate new computational tasks related to such combinations. Thus, we advance the state-of-the-art in fair division of mixed manna.
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We consider a fair division model in which agents have positive, zero and negative utilities for items. For this model, we analyse one existing fairness property - EFX - and three new and related properties - EFX$_0$, EFX$^3$ and EF1$^3$ - in combination with Pareto-optimality. With general utilities, we give a modified version of an existing algorithm for computing an EF1$^3$ allocation. With $-alpha/0/alpha$ utilities, this algorithm returns an EFX$^3$ and PO allocation. With absolute identical utilities, we give a new algorithm for an EFX and PO allocation. With $-alpha/0/beta$ utilities, this algorithm also returns such an allocation. We report some new impossibility results as well.
We consider a multi-agent model for fair division of mixed manna (i.e. items for which agents can have positive, zero or negative utilities), in which agents have additive utilities for bundles of items. For this model, we give several general impossibility results and special possibility results for three common fairness concepts (i.e. EF1, EFX, EFX3) and one popular efficiency concept (i.e. PO). We also study how these interact with common welfare objectives such as the Nash, disutility Nash and egalitarian welfares. For example, we show that maximizing the Nash welfare with mixed manna (or minimizing the disutility Nash welfare) does not ensure an EF1 allocation whereas with goods and the Nash welfare it does. We also prove that an EFX3 allocation may not exist even with identical utilities. By comparison, with tertiary utilities, EFX and PO allocations, or EFX3 and PO allocations always exist. Also, with identical utilities, EFX and PO allocations always exist. For these cases, we give polynomial-time algorithms, returning such allocations and approximating further the Nash, disutility Nash and egalitarian welfares in special cases.
We study the fair division of items to agents supposing that agents can form groups. We thus give natural generalizations of popular concepts such as envy-freeness and Pareto efficiency to groups of fixed sizes. Group envy-freeness requires that no group envies another group. Group Pareto efficiency requires that no group can be made better off without another group be made worse off. We study these new group properties from an axiomatic viewpoint. We thus propose new fairness taxonomies that generalize existing taxonomies. We further study ne
We consider fair division problems where indivisible items arrive one-by-one in an online fashion and are allocated immediately to agents who have additive utilities over these items. Many existing offline mechanisms do not work in this online setting. In addition, many existing axiomatic results often do not transfer from the offline to the online setting. For this reason, we propose here three new online mechanisms, as well as consider the axiomatic properties of three previously proposed online mechanisms. In this paper, we use these mechanisms and characterize classes of online mechanisms that are strategy-proof, and return envy-free and Pareto efficient allocations, as well as combinations of these properties. Finally, we identify an important impossibility result.
We consider the problem of fairly allocating indivisible goods, among agents, under cardinality constraints and additive valuations. In this setting, we are given a partition of the entire set of goods---i.e., the goods are categorized---and a limit is specified on the number of goods that can be allocated from each category to any agent. The objective here is to find a fair allocation in which the subset of goods assigned to any agent satisfies the given cardinality constraints. This problem naturally captures a number of resource-allocation applications, and is a generalization of the well-studied (unconstrained) fair division problem. The two central notions of fairness, in the context of fair division of indivisible goods, are envy freeness up to one good (EF1) and the (approximate) maximin share guarantee (MMS). We show that the existence and algorithmic guarantees established for these solution concepts in the unconstrained setting can essentially be achieved under cardinality constraints. Specifically, we develop efficient algorithms which compute EF1 and approximately MMS allocations in the constrained setting. Furthermore, focusing on the case wherein all the agents have the same additive valuation, we establish that EF1 allocations exist and can be computed efficiently even under laminar matroid constraints.
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