  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.
