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Almost Envy-Free Allocations with Connected Bundles

Vittorio Bilò, Ioannis Caragiannis, Michele Flammini, Ayumi Igarashi, Gianpiero Monaco, Dominik Peters, Cosimo Vinci, William S. Zwicker, Michael Wagner
2018 Innovations in Theoretical Computer Science  
We study the existence of allocations of indivisible goods that are envy-free up to one good (EF1), under the additional constraint that each bundle needs to be connected in an underlying item graph G.  ...  Our positive results for paths imply the existence of connected EF1 or EF2 allocations whenever G is traceable, i.e., contains a Hamiltonian path.  ...  I T C S 2 0 1 9 14:4 Almost Envy-Free Allocations with Connected Bundles allocation of a path into bundles that have a constant number of connected components.  ... 
doi:10.4230/lipics.itcs.2019.14 dblp:conf/innovations/BiloCFIMPVZ19 fatcat:julkjuspr5dxdjzlvsb3axhtqq

Almost Envy-Free Allocations with Connected Bundles [article]

Vittorio Bilò, Ioannis Caragiannis, Michele Flammini, Ayumi Igarashi, Gianpiero Monaco, Dominik Peters, Cosimo Vinci, William S. Zwicker
2018 arXiv   pre-print
We study the existence of allocations of indivisible goods that are envy-free up to one good (EF1), under the additional constraint that each bundle needs to be connected in an underlying item graph G.  ...  Our positive results for paths imply the existence of connected EF1 or EF2 allocations whenever G is traceable, i.e., contains a Hamiltonian path.  ...  leaves the envied bundle connected.  ... 
arXiv:1808.09406v1 fatcat:qssvgwctmzd43jask6nldshrta

Envy, Multi Envy, and Revenue Maximization [article]

Amos Fiat, Amiram Wingarten
2009 arXiv   pre-print
We define an allocation/pricing as multi envy free if no agent wishes to replace her allocation with the union of the allocations of some set of other agents and her price with the sum of their prices.  ...  We study the envy free pricing problem faced by a seller who wishes to maximize revenue by setting prices for bundles of items.  ...  By condition 1 of the arcs definition an agent can be allocated with her entire bundle or with an empty bundle.  ... 
arXiv:0909.4569v1 fatcat:uif4k3bs2rbkxfhvpzm7hi35cq

Fair division of graphs and of tangled cakes [article]

Ayumi Igarashi, William S. Zwicker
2021 arXiv   pre-print
We explore which tangles guarantee envy-free allocations of connected shares for n agents, meaning that such allocations exist no matter which monotonic and continuous functions represent agents' valuations  ...  An elaboration of Stromquist's moving knife procedure shows that the non-stringable lips tangle guarantees envy-free allocations of connected shares for three agents.  ...  guarantee connected envy-free allocations of the lips tangle L for three agents.  ... 
arXiv:2102.08560v1 fatcat:gie4facmybaavasqn7uqfslyd4

Fairness and fuzzy coalitions

Chiara Donnini, Marialaura Pesce
2021 International Journal of Game Theory  
We propose a notion of fairness which, besides efficiency, imposes absence of envy towards fuzzy coalitions, and which fully characterizes competitive equilibria and Aubin-core allocations.  ...  AbstractIn this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy á la Shitovitz (Econometrica 41:467–501, 1973), with agents' measure space having both  ...  An allocation x is strictly envy-free (or strictly equitable) if almost every agent does not envy any (standard) coalition.  ... 
doi:10.1007/s00182-021-00780-2 fatcat:dmc2x3efhvcy5jw52ffuxmt7mq

Revenue Maximizing Envy-Free Pricing in Matching Markets with Budgets [article]

Riccardo Colini-Baldeschi and Stefano Leonardi and Qiang Zhang
2016 arXiv   pre-print
We study envy-free pricing mechanisms in matching markets with m items and n budget constrained buyers.  ...  Our goal is to compute an envy-free pricing allocation that maximizes the revenue, i.e., the total payment charged to the buyers.  ...  Thus in a bundle-price envy-free allocation no buyer has an incentive to barter her bundle with the bundle of someone else.  ... 
arXiv:1610.09221v1 fatcat:xrb56ipsabddleabungpfatjhe

One Dollar Each Eliminates Envy [article]

Johannes Brustle and Jack Dippel and Vishnu V. Narayan and Mashbat Suzuki and Adrian Vetta
2019 arXiv   pre-print
Further, we prove that for general monotonic valuation functions an envy-free allocation always exists with a subsidy of at most 2(n-1) dollars per agent.  ...  In fact, a subsidy of at most one dollar per agent is sufficient to guarantee the existence of an envy-free allocation.  ...  Almost envy-free allocations with connected bundles. In Proceedings of 10th Innovations in Theoretical Computer Science Conference (ITCS), pages 14:1–14:21, 2019. [5] S. Brams and A. Taylor.  ... 
arXiv:1912.02797v1 fatcat:orvzknnjtnec3n23nsvu77lqra

Almost Envy Freeness and Welfare Efficiency in Fair Division with Goods or Bads [article]

Martin Aleksandrov
2018 arXiv   pre-print
For example, with additive identical valuations, an allocation that maximizes the egalitarian diswelfare or Nash diswelfare is XEF and PE.  ...  Finally, we also give simple and tractable cases when these envy freeness proxies and welfare efficiency are attainable in combination (e.g. binary valuations, house allocations).  ...  We say that an allocation A is envy free (EF) iff, for each i, j ∈ N , u i (A i ) ≥ u i (A j ).  ... 
arXiv:1808.00422v2 fatcat:pr5sqf62fvh3vnyxhluoutzp4a

Fair Division with Bounded Sharing [article]

Erel Segal-Halevi
2019 arXiv   pre-print
A set of objects is to be divided fairly among agents with different tastes, modeled by additive value functions.  ...  The paper studies various notions of fairness, such as proportionality, envy-freeness and equitability.  ...  For general cakes, connected envy-free allocations cannot be found using a finite number of queries (Stromquist, 2008) .  ... 
arXiv:1912.00459v1 fatcat:r74uasbvbbejlgoypptey2kzmq

On Fair Division under Heterogeneous Matroid Constraints [article]

Amitay Dror, Michal Feldman, Erel Segal-Halevi
2022 arXiv   pre-print
Previous algorithms for finding EF1 allocations are either restricted to agents with identical feasibility constraints, or allow free disposal of items.  ...  In these settings, every agent is restricted to get a bundle among a specified set of feasible bundles.  ...  In the example above, the best feasible subset of Bob's bundle for Alice is worth 3. Thus, the allocation is feasibly-envy-free (F-EF).  ... 
arXiv:2010.07280v4 fatcat:zxbatsyl5rff3ioqlnlbm7gcd4

Almost Envy-Freeness in Group Resource Allocation

Maria Kyropoulou, Warut Suksompong, Alexandros A. Voudouris
2019 Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence  
can be guaranteed with respect to both envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX).  ...  We study the problem of fairly allocating indivisible goods between groups of agents using the recently introduced relaxations of envy-freeness.  ...  An allocation is said to be envy-free if it is envy-free for every agent.  ... 
doi:10.24963/ijcai.2019/57 dblp:conf/ijcai/KyropoulouSV19 fatcat:civldzd3d5artaclcdo5znj2oa

On the Number of Almost Envy-Free Allocations [article]

Warut Suksompong
2020 arXiv   pre-print
Envy-freeness is a standard benchmark of fairness in resource allocation.  ...  Since it cannot always be satisfied when the resource consists of indivisible items even when there are two agents, the relaxations envy-freeness up to one item (EF1) and envy-freeness up to any item (  ...  A bundle M ′ is said to be • envy-free up to one item (EF1) for agent i, if either u i (M ′ ) ≥ u i (M \M ′ ), or there exists an item j ∈ M \M ′ such that u i (M ′ ) ≥ u i (M \(M ′ ∪ {j})); • envy-free  ... 
arXiv:2006.00178v1 fatcat:vnfubjqwyfcfpmfpmfn7bbsd7u

Almost Envy-freeness, Envy-rank, and Nash Social Welfare Matchings [article]

Alireza Farhadi, MohammadTaghi Hajiaghayi, Mohamad Latifian, Masoud Seddighin, Hadi Yami
2020 arXiv   pre-print
Envy-free up to one good (EF1) and envy-free up to any good (EFX) are two well-known extensions of envy-freeness for the case of indivisible items.  ...  For our algorithm, we introduce Nash Social Welfare Matching which makes a connection between Nash Social Welfare and envy freeness.  ...  In addition, assume that the bundle allocated to an agent j contains two items, each with value 600 to agent i.  ... 
arXiv:2007.07027v1 fatcat:a3wr6btjnrfifd4gandqf3moli

Comparing Approximate Relaxations of Envy-Freeness

Georgios Amanatidis, Georgios Birmpas, Vangelis Markakis
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
In fair division problems with indivisible goods it is well known that one cannot have any guarantees for the classic fairness notions of envy-freeness and proportionality.  ...  In this work, we investigate further the connections between the four notions mentioned above and their approximate versions.  ...  An allocation A = (A 1 , . . . , A n ) is envy-free (EF), if for every i, j ∈ N , v i (A i ) ≥ v i (A j ).  ... 
doi:10.24963/ijcai.2018/6 dblp:conf/ijcai/AmanatidisBM18 fatcat:jtimorlwknbn5hzw7escssl4gq

Fair Division through Information Withholding [article]

Hadi Hosseini, Sujoy Sikdar, Rohit Vaish, Jun Wang, Lirong Xia
2020 arXiv   pre-print
We study allocations that are nearly envy-free in aggregate, and define a novel fairness notion based on information withholding.  ...  Under this notion, an agent can withhold (or hide) some of the goods in its bundle and reveal the remaining goods to the other agents.  ...  We are grateful to Ariel Procaccia and Nisarg Shah for sharing with us the data from Spliddit, and to Haris Aziz for bringing to our attention the proof of EF E for binary valuations in (Aziz et al.,  ... 
arXiv:1907.02583v3 fatcat:geuiytxucrdfddwdqyxqzb4bda
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