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 dis- tribution 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 probabil- ity model — there is a lottery over preference profiles. For each of the models, we study the computational complexity of computing the sta- bility 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.
['Haris Aziz', 'Péter Biró', 'Serge Gaspers', 'Ronald de Haan', 'Nicholas Mattei', 'Baharak Rastegari']
Stable Matching with Uncertain Linear Preferences