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.

中文翻译：

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稳定婚姻中的贿赂与控制

我们通过考虑几种操纵行为以及几个“理想的”操纵目标，开始研究稳定婚姻中的外部操纵。例如，一个目标是确保给定的一对代理在稳定的解决方案中匹配，这可以通过对某些代理的偏好列表重新排序的操作来实现。我们对以这种方式出现的所有问题的计算复杂性进行了全面的研究。我们发现了几个多项式时间可解的情况以及 NP 难的情况。对于 NP-hard 情况，关注自然参数“预算”（即操作次数），我们还进行了参数化复杂度分析并遇到了参数化硬度结果。