# 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…

## 6 Citations

A Study of Incentive Compatibility and Stability Issues in Fractional Matchings

- EconomicsAAMAS
- 2020

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

- Computer Science, MathematicsDiscrete Applied Mathematics
- 2022

On the Coexistence of Stability and Incentive Compatibility in Fractional Matchings

- Economics
- 2020

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

- Economics, MathematicsIJCAI
- 2021

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

- Economics, Computer ScienceArXiv
- 2020

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

- EconomicsArXiv
- 2020

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.

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