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Relevant bibliographies by topics / Fair-division problems

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Journal articles

Academic literature on the topic 'Fair-division problems'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Fair-division problems"

1

Aleksandrov, Martin, and Toby Walsh. "Online Fair Division: A Survey." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 09 (2020): 13557–62. http://dx.doi.org/10.1609/aaai.v34i09.7081.

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We survey a burgeoning and promising new research area that considers the online nature of many practical fair division problems. We identify wide variety of such online fair division problems, as well as discuss new mechanisms and normative properties that apply to this online setting. The online nature of such fair division problems provides both opportunities and challenges such as the possibility to develop new online mechanisms as well as the difficulty of dealing with an uncertain future.

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2

Herreiner, Dorothea K., and Clemens D. Puppe. "Envy Freeness in Experimental Fair Division Problems." Theory and Decision 67, no. 1 (2007): 65–100. http://dx.doi.org/10.1007/s11238-007-9069-8.

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3

Dall'Aglio, Marco, and Theodore P. Hill. "Maximin share and minimax envy in fair-division problems." Journal of Mathematical Analysis and Applications 281, no. 1 (2003): 346–61. http://dx.doi.org/10.1016/s0022-247x(03)00107-0.

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4

Sagara, Nobusumi. "A characterization of α-maximin solutions of fair division problems". Mathematical Social Sciences 55, № 3 (2008): 273–80. http://dx.doi.org/10.1016/j.mathsocsci.2007.09.007.

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5

Moulin, H. "Fair division under joint ownership: Recent results and open problems." Social Choice and Welfare 7, no. 2 (1990): 149–70. http://dx.doi.org/10.1007/bf01560582.

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6

Vetschera, Rudolf. "A general branch-and-bound algorithm for fair division problems." Computers & Operations Research 37, no. 12 (2010): 2121–30. http://dx.doi.org/10.1016/j.cor.2010.03.001.

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7

Arunachaleswaran, Eshwar Ram, Siddharth Barman, and Nidhi Rathi. "Fair Division with a Secretive Agent." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1732–39. http://dx.doi.org/10.1609/aaai.v33i01.33011732.

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We study classic fair-division problems in a partial information setting. This paper respectively addresses fair division of rent, cake, and indivisible goods among agents with cardinal preferences. We will show that, for all of these settings and under appropriate valuations, a fair (or an approximately fair) division among n agents can be efficiently computed using only the valuations of n − 1 agents. The nth (secretive) agent can make an arbitrary selection after the division has been proposed and, irrespective of her choice, the computed division will admit an overall fair allocation.For the rent-division setting we prove that well-behaved utilities of n − 1 agents suffice to find a rent division among n rooms such that, for every possible room selection of the secretive agent, there exists an allocation (of the remaining n − 1 rooms among the n − 1 agents) which ensures overall envy freeness (fairness). We complement this existential result by developing a polynomial-time algorithm for the case of quasilinear utilities. In this partial information setting, we also develop efficient algorithms to compute allocations that are envy-free up to one good (EF1) and ε-approximate envy free. These two notions of fairness are applicable in the context of indivisible goods and divisible goods (cake cutting), respectively.One of the main technical contributions of this paper is the development of novel connections between different fairdivision paradigms, e.g., we use our existential results for envy-free rent-division to develop an efficient EF1 algorithm.

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8

Goetz, Albert. "Cost Allocation: An Application of Fair Division." Mathematics Teacher 93, no. 7 (2000): 600–603. http://dx.doi.org/10.5951/mt.93.7.0600.

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Although the subject of cost allocation has been extensively discussed in the literature of political economics, it has been generally neglected in mathematical literature. However, cost allocation affords a practical extension of fair-division techniques–one that is readily accessible to secondary school students and that gives them a simple yet powerful application of mathematics to real-world problem solving. A study of the concepts and the mathematics involved in cost allocation is most appropriate in a discrete mathematics course or a modeling course, but a case can be made for including this topic in other courses, as well. This article presents a typical cost-allocation problem with possible solutions and includes suggestions for presenting similar problems in the classroom. The basics of the problem follow closely from Young (1994).

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9

Bei, Xiaohui, Ayumi Igarashi, Xinhang Lu, and Warut Suksompong. "The Price of Connectivity in Fair Division." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 6 (2021): 5151–58. http://dx.doi.org/10.1609/aaai.v35i6.16651.

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We study the allocation of indivisible goods that form an undirected graph and quantify the loss of fairness when we impose a constraint that each agent must receive a connected subgraph. Our focus is on the well-studied fairness notion of maximin share fairness. We introduce the price of connectivity to capture the largest gap between the graph-specific and the unconstrained maximin share, and derive bounds on this quantity which are tight for large classes of graphs in the case of two agents and for paths and stars in the general case. For instance, with two agents we show that for biconnected graphs it is possible to obtain at least 3/4 of the maximin share with connected allocations, while for the remaining graphs the guarantee is at most 1/2. Our work demonstrates several applications of graph-theoretic tools and concepts to fair division problems.

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10

Dror, Amitay, Michal Feldman, and Erel Segal-Halevi. "On Fair Division under Heterogeneous Matroid Constraints." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 6 (2021): 5312–20. http://dx.doi.org/10.1609/aaai.v35i6.16670.

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We study fair allocation of indivisible goods among additive agents with feasibility constraints. In these settings, every agent is restricted to get a bundle among a specified set of feasible bundles. Such scenarios have been of great interest to the AI community due to their applicability to real-world problems. Following some impossibility results, we restrict attention to matroid feasibility constraints that capture natural scenarios, such as the allocation of shifts to medical doctors, and the allocation of conference papers to referees. We focus on the common fairness notion of envy-freeness up to one good (EF1). Previous algorithms for finding EF1 allocations are either restricted to agents with identical feasibility constraints, or allow free disposal of items. An open problem is the existence of EF1 complete allocations among heterogeneous agents, where the heterogeneity is both in the agents' feasibility constraints and in their valuations. In this work, we make progress on this problem by providing positive and negative results for different matroid and valuation types. Among other results, we devise poly-time algorithms for finding EF1 allocations in the following settings: (i) n agents with heterogeneous partition matroids and heterogeneous binary valuations, (ii) 2 agents with heterogeneous partition matroids and heterogeneous valuations, and (iii) at most 3 agents with heterogeneous binary valuations and identical base-orderable matroids.

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