Bribery and Control in Stable Marriage

Abstract

We initiate the study of external manipulations in Stable Marriage by considering  several manipulative actions as well as several manipulation goals. For instance, one goal  is to make sure that a given pair of agents is matched in a stable solution, and this may be  achieved by the manipulative action of reordering some agents' preference lists. We present  a comprehensive study of the computational complexity of all problems arising in this way.  We find several polynomial-time solvable cases as well as NP-hard ones. For the NP-hard  cases, focusing on the natural parameter "budget" (that is, the number of manipulative  actions one is allowed to perform), we also conduct a parameterized complexity analysis  and encounter mostly parameterized hardness results.