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.
Recent work by Aziz et al. REF looked at the stable matching problem in settings where there is uncertainty about the preferences of the agents.
Stable Matching with Uncertain Linear Preferences
ArXiv
ArXiv
Mathematics Computer Science