Stable Matching with Uncertain Linear Preferences
Abstract
We consider the two-sided stable matching setting in which there may be uncertainty about the agents' preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model --- in which for each agent, there is a probability distribution over linear preferences, (2) compact indifference model --- for each agent, a weak preference order is specified and each linear order compatible with the weak order is equally likely and (3) joint probability model --- there is a lottery over preference profiles. For each of the models, we study the computational complexity of computing the stability probability of a given matching as well as finding a matching with the highest probability of being stable. We also examine more restricted problems such as deciding whether a certainly stable matching exists. We find a rich complexity landscape for these problems, indicating that the form uncertainty takes is significant.
Cite
@article{arxiv.1607.02917,
title = {Stable Matching with Uncertain Linear Preferences},
author = {Haris Aziz and Péter Biró and Serge Gaspers and Ronald de Haan and Nicholas Mattei and Baharak Rastegari},
journal= {arXiv preprint arXiv:1607.02917},
year = {2016}
}
Comments
A preliminary version of this paper has been accepted for publication in the proceedings of the 9th International Symposium on Algorithmic Game Theory (SAGT 2016)