加权投票博弈中权力与比例的最坏情况界及其在假名操纵中的应用
Worst-case Bounds on Power vs. Proportion in Weighted Voting Games with Application to False-name Manipulation
摘要：
加权投票游戏适用于各种各样的多智能体设置。它们使权力指数的形式化，量化了球员的联盟力量。我们采用一种新颖的方法来研究大与小的力量。这些游戏中的小玩家我们将小（大）玩家建模为具有单（多）票。大玩家的总体相对权力是以~投票比例。对于这个比率，我们显示小常数的Shapley-Shubik和Deegan-Packel指数的最坏情况下的界限。与此形成鲜明对比的是，这个比例是无界的Banzhaf指数。作为应用，我们定义了一个假名策略范式博弈，其中每个大玩家可以在虚假身份之间分配其选票，并研究了它的各种性质。总之，我们的研究结果提供了基础的影响球员的大小，建模为他们的分裂能力，对他们的相对权力。
英文摘要：
Weighted voting games apply to a wide variety of multi-agent settings. They enable the formalization of power indices which quantify the coalitional power of players. We take a novel approach to the study of the power of big vs.~small players in these games. We model small (big) players as having single (multiple) votes. The aggregate relative power of big players is measured w.r.t.~their votes proportion. For this ratio, we show small constant worst-case bounds for the Shapley-Shubik and the Deegan-Packel indices. In sharp contrast, this ratio is unbounded for the Banzhaf index. As an application, we define a false-name strategic normal form game where each big player may split its votes between false identities, and study its various properties. Together, our results provide foundations for the implications of players' size, modeled as their ability to split, on their relative power.
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