Stable Fractional Matchings

@article{Caragiannis2019StableFM,
  title={Stable Fractional Matchings},
  author={Ioannis Caragiannis and Aris Filos-Ratsikas and Panagiotis Kanellopoulos and Rohit Vaish},
  journal={Proceedings of the 2019 ACM Conference on Economics and Computation},
  year={2019}
}
We study a generalization of the classical stable matching problem that allows for cardinal preferences (as opposed to ordinal) and fractional matchings (as opposed to integral). After observing that, in this cardinal setting, stable fractional matchings can have much higher social welfare than stable integral ones, our goal is to understand the computational complexity of finding an optimal (i.e., welfare-maximizing) or nearly-optimal stable fractional matching. We present simple approximation… 
View on ACM
repository.essex.ac.uk
6 Citations
Highly Influential Citations
2
Background Citations
3

Figures from this paper

6 Citations

Citation Type

Citation Type

A Study of Incentive Compatibility and Stability Issues in Fractional Matchings
TLDR
This paper reports the first investigation into the important but unexplored topic of incentive compatibility of matching mechanisms to find stable fractional matchings, focusing on matching instances under strict preferences.
Maximum 0-1 Timed Matching on Temporal Graphs
On the Coexistence of Stability and Incentive Compatibility in Fractional Matchings
Stable matchings have been studied extensively in social choice literature. The focus has been mostly on integral matchings, in which the nodes on the two sides are wholly matched. A fractional…
Fractional Matchings under Preferences: Stability and Optimality
TLDR
A generalized version of the classic Stable Marriage and Stable Roommates problems where agents may share partners is studied, obtaining a complete picture regarding the computational complexity of finding an optimal ordinally stable or cardinally stable matching.
On Achieving Fairness and Stability in Many-to-One Matchings
TLDR
This work is the first to address the problem of finding a leximin optimally fair and stable matching and shows that finding such a matching is NP-Hard, even under isometric utilities.
The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints
TLDR
While VER always returns a stable and constrained efficient allocation, it fails to be strategyproof, unconstrained efficient, and envy-free, and it is shown that each of these three properties is incompatible with stability and constrained efficiency.

References

SHOWING 1-10 OF 85 REFERENCES
Stable fractional matchings
A Study of Incentive Compatibility and Stability Issues in Fractional Matchings
TLDR
This paper reports the first investigation into the important but unexplored topic of incentive compatibility of matching mechanisms to find stable fractional matchings, focusing on matching instances under strict preferences.
Anarchy, stability, and utopia: creating better matchings
TLDR
The loss in social welfare that arises from requiring matchings to be stable, the natural equilibrium concept under individual rationality, is examined, and it is proved worst case bounds on the price of anarchy are proved.
Stable Matchings, Optimal Assignments, and Linear Programming
TLDR
It is shown that those fractional matchings in the Stable Marriage Polytope form a lattice with respect to a partial ordering that involves stochastic dominance, and all expected utility functions corresponding to the same ordinal preferences will agree on the relevant comparisons.
Stable Marriage and Indifference
Elicitation and Approximately Stable Matching with Partial Preferences
TLDR
This work proposes the use of maximum regret to measure the degree of stability of a matching with partial preferences; minimax regret to find matchings that are maximally stable in the presence ofpartial preferences; and heuristic elicitation schemes that use max regret to determine relevant preference queries.
Fractional solutions for capacitated NTU-games, with applications to stable matchings
The Geometry of Fractional Stable Matchings and Its Applications
TLDR
It is shown that a related geometry allows us to express any fractional solution in the stable marriage polytope as a convex combination of stable marriage solutions, which leads to a genuinely simple proof of the integrality of the stablemarriage polytopes.
A Natural Generalization of Stable Matching Solved via New Insights into Ideal Cuts
We study a natural generalization of stable matching to the maximum weight stable matching problem and we obtain a combinatorial polynomial time algorithm for it by reducing it to the problem of…
Stability and the Core of Probabilistic Marriage Problems
We study the marriage problem where a probability distribution over matchings is chosen. The “core” has been central to the the analysis of the deterministic problem. This is particularly the case…
...
1
2
3
4
5
...