Weighted voting games are a well-studied class of succinct simple games that can be used to model collective decision-making in, e.g., legislative bodies such as parliaments and shareholder voting. Power indices [1,2,3,4] are used to measure the influence of players in weighted voting games. In such games, it has been studied how a distinguished player’s power can be changed, e.g., by merging or splitting players (the latter is a.k.a. false-name manipulation) [5, 6], by changing the quota [7], or via structural control by adding or deleting players [8]. We continue the work on the structural control initiated by Rey and Rothe [8] by solving some of their open problems. In addition, we also modify their model to a more realistic setting in which the quota is indirectly changed during the addition or deletion of players (in a different sense than that of Zuckerman et al. [7] who manipulate the quota directly without changing the set of players), and we study the corresponding problems in terms of their computational complexity.

加权投票博弈是一类经过充分研究的简洁简单博弈，可用于对议会和股东投票等立法机构中的集体决策进行建模。权力指数[1,2,3,4]用于衡量加权投票游戏中玩家的影响力。在此类游戏中，人们已经研究了如何改变杰出玩家的权力，例如，通过合并或分裂玩家（后者又名假名操纵）[5, 6]，通过改变配额[7]，或通过通过添加或删除玩家进行结构控制[8]。我们继续研究 Rey 和 Rothe [8] 发起的结构控制工作，解决他们的一些开放性问题。此外，