Bribery and Control in Stable Marriage

Abstract

We initiate the study of external manipulations in Stable Marriage by considering\xa0 several manipulative actions as well as several manipulation goals. For instance, one goal\xa0 is to make sure that a given pair of agents is matched in a stable solution, and this may be\xa0 achieved by the manipulative action of reordering some agents preference lists. We present\xa0 a comprehensive study of the computational complexity of all problems arising in this way.\xa0 We find several polynomial-time solvable cases as well as NP-hard ones. For the NP-hard\xa0 cases, focusing on the natural parameter budget (that is, the number of manipulative\xa0 actions one is allowed to perform), we also conduct a parameterized complexity analysis\xa0 and encounter mostly parameterized hardness results.\xa0