Envy-Freeness in House Allocation Problems

@article{Gan2019EnvyFreenessIH,
  title={Envy-Freeness in House Allocation Problems},
  author={Jiarui Gan and Warut Suksompong and Alexandros A. Voudouris},
  journal={Math. Soc. Sci.},
  year={2019},
  volume={101},
  pages={104-106}
}
We consider the house allocation problem, where $m$ houses are to be assigned to $n$ agents so that each agent gets exactly one house. We present a polynomial-time algorithm that determines whether an envy-free assignment exists, and if so, computes one such assignment. We also show that an envy-free assignment exists with high probability if the number of houses exceeds the number of agents by a logarithmic factor. 
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References

SHOWING 1-10 OF 16 REFERENCES
Local envy-freeness in house allocation problems
We study the fair division problem consisting in allocating one item per agent so as to avoid (or minimize) envy, in a setting where only agents connected in a given network may experience envy. In aExpand
Pareto Optimality in House Allocation Problems
TLDR
The concept of a signature is introduced, which allows us to give a characterization, checkable in linear time, of instances that admit a unique Pareto optimal matching. Expand
Pareto Optimality in House Allocation Problems
TLDR
The concept of a signature is introduced, which allows us to give a characterization, checkable in linear time, of instances that admit a unique Pareto optimal matching. Expand
The Efficient Allocation of Individuals to Positions
In a variety of contexts, individuals must be allocated to positions with limited capacities. Legislators must be assigned to committees, college students to dormitories, and urban homesteaders toExpand
On a conjecture by gale about one-sided matching problems
Abstract This paper proves the following result on one-sided matching problems: when there are n objects to be assigned to n agents, for n ⩾3, there exits no mechanism that satisfies symmetry, ParetoExpand
Approximation Algorithms for Computing Maximin Share Allocations
TLDR
It is proved that in randomly generated instances, with high probability there exists a maximin share allocation, which can be seen as a justification of the experimental evidence reported in [5, 14], that maximin sharing allocations exist almost always. Expand
Approximation Algorithms for Computing Maximin Share Allocations
TLDR
It is proved that in randomly generated instances, maximin share allocations exist with high probability, and this improves upon the algorithm of Procaccia and Wang (2014), which is also a 2/3-approximation but runs in polynomial time only for a constant number of agents. Expand
RANDOM SERIAL DICTATORSHIP AND THE CORE FROM RANDOM ENDOWMENTS IN HOUSE ALLOCATION PROBLEMS
Random serial dictatorship and the core from random endowments in house allocation problems
Bipartite Envy-Free Matching
TLDR
This paper presents sufficient and necessary conditions for the existence of a non-empty bipartite Envy-Free Matching, based on cardinality of neighbor-sets, similarly to Hall's condition for theexistence of a perfect matching. Expand
Algorithmics of Matching Under Preferences
TLDR
This book builds on the author’s prior research in this area, and also his practical experience of developing algorithms for matching kidney patients to donors in the UK, for assigning medical students to hospitals in Scotland, and for allocating students to elective courses and projects. Expand
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