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Optimal Proportional Cake Cutting with Connected Pieces

Xiaohui Bei, Ning Chen, Xia Hua, Biaoshuai Tao, Endong Yang
2021 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We study computational complexity of computing an efficiency optimal division given the conditions that the allocation satisfies proportional fairness and assigns each agent a connected piece.  ...  We consider the classic cake cutting problem where one allocates a divisible cake to n participating agents. Among all valid divisions, fairness and efficiency (a.k.a.  ...  (Aumann and Dombb 2010) followed the notion of price of fairness and focused on divisions with only connected pieces.  ... 
doi:10.1609/aaai.v26i1.8243 fatcat:2jtyct5vubhxrfculgtaniz6l4

Resource-monotonicity and Population-monotonicity in Connected Cake-cutting [article]

Erel Segal-Halevi, Balázs Sziklai
2017 arXiv   pre-print
In the classic cake-cutting problem (Steinhaus, 1948), a heterogeneous resource has to be divided among n agents with different valuations in a proportional way --- giving each agent a piece with a value  ...  Classic cake-cutting protocols are neither RM nor PM. Moreover, we prove that no Pareto-optimal proportional division rule can be either RM or PM.  ...  In contrast, with connectivity, the Nash-optimal rule is not proportional.  ... 
arXiv:1703.08928v3 fatcat:spg6hpuw4fhopmfrxkihxe5ihm

Monotonicity and competitive equilibrium in cake-cutting

Erel Segal-Halevi, Balázs R. Sziklai
2018 Economic Theory  
We study the monotonicity properties of solutions in the classic problem of fair cake-cutting --- dividing a heterogeneous resource among agents with different preferences.  ...  We formally introduce these concepts to the cake-cutting problem and examine whether they are satisfied by various common division rules.  ...  Each of our connected division rules satisfies three of the four properties {PROP,WPO,RM,PM}.  ... 
doi:10.1007/s00199-018-1128-6 fatcat:y2nzq6aegbfndd2wekjmlibui4

The Efficiency of Fair Division with Connected Pieces [chapter]

Yonatan Aumann, Yair Dombb
2010 Lecture Notes in Computer Science  
Here, we consider the setting where each player must receive a single connected piece.  ...  We consider the issue of fair division of goods, using the cake cutting abstraction, and aim to bound the possible degradation in social welfare due to the fairness requirements.  ...  For every cake-cutting instance there exists an equitable division of the cake with connected pieces.  ... 
doi:10.1007/978-3-642-17572-5_3 fatcat:xhkp4gkvnzc33fl7uhyyyz5h2e

The Efficiency of Fair Division with Connected Pieces

Yonatan Aumann, Yair Dombb
2015 ACM Transactions on Economics and Computation  
Here, we consider the setting where each player must receive a single connected piece.  ...  We consider the issue of fair division of goods, using the cake cutting abstraction, and aim to bound the possible degradation in social welfare due to the fairness requirements.  ...  For every cake-cutting instance there exists an equitable division of the cake with connected pieces.  ... 
doi:10.1145/2781776 fatcat:swnissxeb5b4zif5xoebyhrxuq

Dividing connected chores fairly

Sandy Heydrich, Rob van Stee
2015 Theoretical Computer Science  
Previous work has been done on this so-called price of fairness, concerning fair division of cakes and chores with non-connected pieces and of cakes with connected pieces.  ...  We also give the first proof of the existence of equitable divisions for chores with connected pieces.  ...  [2] give a polynomial time approximation scheme for computing optimal proportional cake divisions with connected pieces. Brams et al.  ... 
doi:10.1016/j.tcs.2015.05.041 fatcat:jhkynbvsivdefdqnil24jxq7he

Dividing Connected Chores Fairly [chapter]

Sandy Heydrich, Rob van Stee
2013 Lecture Notes in Computer Science  
Previous work has been done on this so-called price of fairness, concerning fair division of cakes and chores with non-connected pieces and of cakes with connected pieces.  ...  We also give the first proof of the existence of equitable divisions for chores with connected pieces.  ...  [2] give a polynomial time approximation scheme for computing optimal proportional cake divisions with connected pieces. Brams et al.  ... 
doi:10.1007/978-3-642-41392-6_15 fatcat:rtsn7xojdnelxfbuxpm6vb3vyu

Cake cutting

Ariel D. Procaccia
2013 Communications of the ACM  
Computing optimal fair cake divisions with connected pieces is significantly harder [5] , even if we abandon fairness completely and just focus on optimizing welfare [4] .  ...  Let me ask though, with tongue in cheek, how good are optimal cake divisions?  ... 
doi:10.1145/2483852.2483870 fatcat:n3wrlxfqevhhhhnleq4bsr34d4

Fairness and Efficiency in Cake-Cutting with Single-Peaked Preferences [article]

Bhavook Bhardwaj, Rajnish Kumar, Josue Ortega
2020 arXiv   pre-print
We study the cake-cutting problem when agents have single-peaked preferences over the cake.  ...  Finally, we provide simple alternative mechanisms that Pareto dominate that of Wang-Wu, and which achieve envy-freeness or Pareto optimality.  ...  The cake is cut at each of these points, generating up to 3n+1 cake pieces.  ... 
arXiv:2002.03174v3 fatcat:ebams4rzwnho5iwkwi5ycbxin4

Determining a Fair Border

Theodore P. Hill
1983 The American mathematical monthly  
[August-September connectivity of the other pieces. However, a (nonconstructive) cake-cutting result of Dubins and Spanier can be used to help settle the border problem affirmatively.  ...  Again, for cake-cutting, optimal partitions in this second sense always exist [2, Cor. 6.10] but for the border problem they do not exist in general as can be seen from Fig. 2 again with the uniform  ... 
doi:10.1080/00029890.1983.11971254 fatcat:gdfkm7ttevhyfjzyg5ynikhwbe

Determining a Fair Border

Theodore P. Hill
1983 The American mathematical monthly  
[August-September connectivity of the other pieces. However, a (nonconstructive) cake-cutting result of Dubins and Spanier can be used to help settle the border problem affirmatively.  ...  Again, for cake-cutting, optimal partitions in this second sense always exist [2, Cor. 6.10] but for the border problem they do not exist in general as can be seen from Fig. 2 again with the uniform  ... 
doi:10.2307/2975720 fatcat:2gjaxa6w3jgndffffyhlwdwapq

Truthful Fair Division without Free Disposal

Xiaohui Bei, Guangda Huzhang, Warut Suksompong
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
We exhibit a truthful envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist  ...  We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents.  ...  We present a truthful, envy-free, and Pareto optimal cake cutting mechanism (Theorem 6) and a truthful, proportional, and Pareto optimal chore division mechanism (Theorem 7) for any number of agents with  ... 
doi:10.24963/ijcai.2018/9 dblp:conf/ijcai/BeiHS18 fatcat:6syva4yz6ra6xl4e2rhf42c3hq

Obvious Manipulations in Cake-Cutting [article]

Josue Ortega, Erel Segal-Halevi
2019 arXiv   pre-print
In cake-cutting, strategy-proofness is a very costly requirement in terms of fairness: for n=2 it implies a dictatorial allocation, whereas for n > 2 it requires that one agent receives no cake.  ...  that each agent receives 1/n of the cake.  ...  Their mechanism may waste pieces of cake which remain unassigned, something that never occurs with the proportional and NOM mechanism we identify.  ... 
arXiv:1908.02988v2 fatcat:jehkly6m7zfxteuze6bw7wg3ha

Fair Division via Social Comparison [article]

Rediet Abebe, Jon Kleinberg, David Parkes
2018 arXiv   pre-print
We fully characterize the set of graphs for which an oblivious single-cutter protocol-- a protocol that uses a single agent to cut the cake into pieces --admits a bounded protocol with O(n^2) query complexity  ...  In the classical cake cutting problem, a resource must be divided among agents with different utilities so that each agent believes they have received a fair share of the resource relative to the other  ...  Acknowledgements The first author would like to thank Felix Fischer for the introduction to the cake cutting problem.  ... 
arXiv:1611.06589v2 fatcat:qfscqvbzvvgvjpo6cifdegvraq

The Price of Indivisibility in Cake Cutting [article]

Eshwar Ram Arunachaleswaran, Ragavendran Gopalakrishnan
2018 arXiv   pre-print
pieces of cake.  ...  Our results contain bounds for the Price of Indivisibility for utilitarian as well as egalitarian social welfare, and for envy-free cake cutting as well as cake cutting without any fairness constraints  ...  We begin by proving two lower bounds for egalitarian welfare (EW) with connected pieces. L 3.6. ∀i ∈ I (n) : Optimal EW(n, k, i) ≥ 1 n , where I represents the set of all cake cutting instances P .  ... 
arXiv:1801.08341v1 fatcat:w2qqlpozxrdxdjsyv5csi2izfa
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