Stable Matching with Uncertain Linear Preferences [article]

Haris Aziz and Péter Biró and Serge Gaspers and Ronald de Haan and Nicholas Mattei and Baharak Rastegari
2016 arXiv   pre-print
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
more » ... -- 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.
arXiv:1607.02917v1 fatcat:sdz2mmrjzjhg3a5azrcgamk5jq