Reforming an Envy-Free Matching

@inproceedings{Ito2022ReformingAE,
  title={Reforming an Envy-Free Matching},
  author={Takehiro Ito and Yuni Iwamasa and Naonori Kakimura and Naoyuki Kamiyama and Yusuke Kobayashi and Yuta Nozaki and Yoshio Okamoto and Kenta Ozeki},
  booktitle={AAAI Conference on Artificial Intelligence},
  year={2022}
}
We consider the problem of reforming an envy-free matching when each agent is assigned a single item. Given an envy-free matching, we consider an operation to exchange the item of an agent with an unassigned item preferred by the agent that results in another envy-free matching. We repeat this operation as long as we can. We prove that the resulting envy-free matching is uniquely determined up to the choice of an initial envy-free matching, and can be found in polynomial time. We call the… 

Figures from this paper

Graphical House Allocation

The classical house allocation problem involves assigning n houses (or items) to n agents according to their preferences. A key criterion in such problems is satisfying some fairness constraints such

References

SHOWING 1-10 OF 24 REFERENCES

Envy-Free Matchings with Lower Quotas

It is shown that, for this model, deciding the existence of an envy-free matching is NP-hard in general, but solvable in polynomial time if quotas are paramodular.

Envy-freeness and relaxed stability: hardness and approximation algorithms

To ensure guaranteed existence of an optimal critical matching, a new notion of optimality is introduced and studied, namely relaxed stability, and it is shown that every instance admits a critical relaxed stable matching and it can be efficiently computed.

Envy-Freeness in House Allocation Problems

On the Convergence of Swap Dynamics to Pareto-Optimal Matchings

It is shown that in marriage and roommate markets, single-peakedness is not sufficient for this to hold, but the stronger restriction of one-dimensional Euclidean preferences is, and this confirms and extends a conjecture made by Damamme et al. (2015) that convergence to a Pareto-optimal matching is guaranteed in housing markets with single- peaked preferences.

Contiguous Cake Cutting: Hardness Results and Approximation Algorithms

NP-hardness results for various decision problems on the existence of envy-free allocations are established and connections between approximate and exact envy-freeness, as well as between continuous and discrete cake cutting are investigated.

EFX Exists for Three Agents

This paper shows constructively that an EFX allocation always exists for three agents, and falsifies the conjecture by Caragiannis et al. by showing an instance with three agents for which there is a partial E FX allocation with higher Nash welfare than that of any complete EFX allocations.

The lattice of envy-free matchings

A bounded and envy-free cake cutting algorithm

This work considers the well-studied cake cutting problem in which the goal is to find an envy-free allocation of a divisible resource based on queries from agents and reports on the algorithm that resolved the open problem.

Fair Allocation of Indivisible Goods

This chapter focuses on fair division of indivisible goods, and assumes in this chapter that the objects are non-shareable, which means that the same item cannot be allocated to more than one agent.

Matching under Preferences

A survey will focus on algorithmic as well as strategic issues of matching theory, successfully applied to many real-world problems such as matching students to universities, doctors to hospitals, kidney transplant patients to donors, and tenants to houses.