Bribery and Control in Stable Marriage
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We initiate the study of external manipulations in Stable Marriage by considering several manipulative actions as well as several "desirable" 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), we also perform a parameterized complexity analysis and encounter parameterized hardness results.
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