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On the Complexity of Efficiency and Envy-Freeness in Fair Division of Indivisible Goods with Additive Preferences [chapter]

Bart de Keijzer, Sylvain Bouveret, Tomas Klos, Yingqian Zhang
2009 Lecture Notes in Computer Science  
We study the problem of allocating a set of indivisible goods to a set of agents having additive preferences.  ...  We introduce two new important complexity results concerning efficiency and fairness in resource allocation problems: we prove that the problem of deciding whether a given allocation is Pareto-optimal  ...  Moreover, we restrict our study to two particular definitions of efficiency and fairness: Pareto-efficiency (or Pareto-optimality) and envy-freeness.  ... 
doi:10.1007/978-3-642-04428-1_9 fatcat:yxgcwjnybzfyxdvvblajkpgjfy

Fair Division: The Computer Scientist's Perspective [article]

Toby Walsh
2020 arXiv   pre-print
I survey recent progress on a classic and challenging problem in social choice: the fair division of indivisible items.  ...  I discuss how a computational perspective has provided interesting insights into and understanding of how to divide items fairly and efficiently.  ...  This has proved popular in fair division, starting with the work of Lipton et al. [2004] and an attractive relaxation of envy-freeness: envy-freeness up to one good (EF1).  ... 
arXiv:2005.04855v1 fatcat:syhptgav6rh7bcgaguxcriehxu

Variable Elimination in Binary CSPs (Extended Abstract)

Martin C. Cooper, Achref El Mouelhi, Cyril Terrioux
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
We propose new rules and compare them, both theoretically and experimentally. We give optimised algorithms to apply these rules and show that each defines a novel tractable class.  ...  Using our variable-elimination rules in preprocessing allowed us to solve more benchmark problems than without.  ...  This has proved popular in fair division, starting with the work of Lipton et al. [2004] and an attractive relaxation of envy-freeness: envy-freeness up to one good (EF1).  ... 
doi:10.24963/ijcai.2020/691 dblp:conf/ijcai/Walsh20 fatcat:i4h3p6o2tvcl7iu4ah33hk2nr4

Fair Division of Mixed Divisible and Indivisible Goods [article]

Xiaohui Bei, Zihao Li, Jinyan Liu, Shengxin Liu, Xinhang Lu
2020 arXiv   pre-print
We study the problem of fair division when the resources contain both divisible and indivisible goods.  ...  Classic fairness notions such as envy-freeness (EF) and envy-freeness up to one good (EF1) cannot be directly applied to the mixed goods setting.  ...  In the cake-adding phase, if the piece of cake to be allocated is not the whole remaining cake, the sum of all agents' valuation on the remaining cake decreases by at leastǫ. Proof.  ... 
arXiv:1911.07048v2 fatcat:fxerxkqoovbdbiweo3c4yg7h7e

Fair Division of Mixed Divisible and Indivisible Goods

Xiaohui Bei, Zihao Li, Jinyan Liu, Shengxin Liu, Xinhang Lu
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We study the problem of fair division when the resources contain both divisible and indivisible goods.  ...  Classic fairness notions such as envy-freeness (EF) and envy-freeness up to one good (EF1) cannot be directly applied to the mixed goods setting.  ...  Acknowledgments This work is supported in part by an RGC grant (HKU 17203717E).  ... 
doi:10.1609/aaai.v34i02.5548 fatcat:wf2hgv37wvh2hd7qpoicihpfum

Efficiency and Envy-freeness in Fair Division of Indivisible Goods: Logical Representation and Complexity

S. Bouveret, J. Lang
2008 The Journal of Artificial Intelligence Research  
We consider the problem of allocating fairly a set of indivisible goods among agents from the point of view of compact representation and computational complexity.  ...  Then we identify the complexity of determining whether there exists an efficient and envy-free allocation, for several notions of efficiency, when preferences are represented in a succinct way (as well  ...  Acknowledgements: We thank Michel Lemaître for stimulating discussions about fair division and compact representation, and Thibault Gajdos for stimulating discussions about envy-freeness and for pointing  ... 
doi:10.1613/jair.2467 fatcat:oci5j6yeqvhr7hoogvc7rdqigq

Online Fair Division: A Survey [article]

Martin Aleksandrov, Toby Walsh
2019 arXiv   pre-print
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  ...  We survey a burgeoning and promising new research area that considers the online nature of many practical fair division problems.  ...  Acknowledgments The authors are funded by the European Research Council under the Horizon 2020 Programme via an Advanced Research Grant AMPLify 670077.  ... 
arXiv:1911.09488v1 fatcat:budywg7q25f5zpby6j7ji2r7ty

Online Fair Division: A Survey

Martin Aleksandrov, Toby Walsh
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
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  ...  We survey a burgeoning and promising new research area that considers the online nature of many practical fair division problems.  ...  Acknowledgments The authors are funded by the European Research Council under the Horizon 2020 Programme via an Advanced Research Grant AMPLify 670077.  ... 
doi:10.1609/aaai.v34i09.7081 fatcat:3emcuwamg5emphe5pevygbxtq4

Negotiation criteria for multiagent resource allocation

Karthik Iyer, Michael N. Huhns
2009 Knowledge engineering review (Print)  
The criteria are organized into five categories. The allocation category contains criteria concerning fairness and envy-freeness with respect to how resources are allocated to agents.  ...  We group the criteria based on how they relate to each other as well as their historical origin. In addition, we present three new criteria: verifiability, dimensionality, and topology.  ...  Their detailed comments on each aspect of the paper helped us in presenting this material in a clear and succinct manner.  ... 
doi:10.1017/s0269888909000204 fatcat:wz64tq5l3vhyrl7mdmjjwgcsjm

Lecture Notes on Fair Division [article]

Ulle Endriss
2018 arXiv   pre-print
Fair division is the problem of dividing one or several goods amongst two or more agents in a way that satisfies a suitable fairness criterion.  ...  While the classical literature on fair division has largely developed within Economics, these Notes are specifically written for readers with a background in Computer Science or similar, and who may be  ...  Sometimes there are both divisible and indivisible goods; a typical example is the case of fair division with a set of indivisible goods and money (a divisible resource).  ... 
arXiv:1806.04234v1 fatcat:vcpq7kqkzrbitm6mhq5orqwzjy

Developments in Multi-Agent Fair Allocation [article]

Haris Aziz
2020 arXiv   pre-print
I survey some recent developments in the field of multi-agent fair allocation.  ...  Fairness is becoming an increasingly important concern when designing markets, allocation procedures, and computer systems.  ...  The author thanks Alex Lam and the reviewers for useful comments.  ... 
arXiv:1911.09852v2 fatcat:mo22colwpjc3ppux2yo2mszt7u

Developments in Multi-Agent Fair Allocation

Haris Aziz
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
I survey some recent developments in the field of multi-agent fair allocation.  ...  Fairness is becoming an increasingly important concern when designing markets, allocation procedures, and computer systems.  ...  Acknowledgements The survey is based on a presentation given by the author at the Dagstuhl-Seminar on Application-Oriented Computational Social Choice (Seminar Number 19381).  ... 
doi:10.1609/aaai.v34i09.7082 fatcat:lobgo7h5k5co5pqojnbfwmgji4

Distributed fair allocation of indivisible goods

Yann Chevaleyre, Ulle Endriss, Nicolas Maudet
2017 Artificial Intelligence  
Distributed mechanisms for allocating indivisible goods are mechanisms lacking central control, in which agents can locally agree on deals to exchange some of the goods in their possession.  ...  We also introduce an extension of the basic framework where agents are vertices of a graph limiting which agents can interact with each other and prove a similar convergence result for envy-freeness in  ...  If agents can receive sets of goods, and if their preferences over the goods are not additively separable, then fair division becomes a combinatorial optimisation problem.  ... 
doi:10.1016/j.artint.2016.09.005 fatcat:5r2s4stutnbmbjhwh3frqjk5xm

Simultaneous Cake Cutting

Eric Balkanski, Simina Brânzei, David Kurokawa, Ariel Procaccia
2014 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We introduce the simultaneous model for cake cutting (the fair allocation of a divisible good), in which agents simultaneously send messages containing a sketch of their preferences over the cake.  ...  Cake divisions satisfying another prominent fairness notion, envy-freeness, are impossible to compute in the simultaneous model, but admit arbitrarily good approximations.  ...  Our Results Our results focus on the two most widely-studied fairness properties, proportionality and envy-freeness.  ... 
doi:10.1609/aaai.v28i1.8802 fatcat:fwhaibpff5bn7cfxcoc2hzmyd4

Algorithmic Fair Allocation of Indivisible Items: A Survey and New Questions [article]

Haris Aziz, Bo Li, Herve Moulin, Xiaowei Wu
2022 arXiv   pre-print
Particularly, in this survey, we focus on indivisible items, for which absolute fairness such as envy-freeness and proportionality cannot be guaranteed.  ...  The theory of algorithmic fair allocation is within the center of multi-agent systems and economics in the last decade due to its industrial and social importance.  ...  Fairness is mostly captured by envy-freeness and proportionality in the literature.  ... 
arXiv:2202.08713v1 fatcat:kovxtvlrkngt3fgamxbxkax2aa
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