加权投票博弈中的假名操纵
False-Name Manipulations in Weighted Voting Games
摘要：
加权投票是决策领域中智能体之间合作的经典模型。在这种游戏中，每个玩家都有一个权重，如果玩家的总权重达到或超过给定的配额，则玩家联盟赢得游戏。在这类博弈中，博弈者的权力通常与其体重不成正比，而是通过权力指数来衡量的，其中最突出的是Shapley-Shubik指数和Banzhaf指数。本文研究了博弈者通过假名操纵，即，通过改变自己的权力，可以改变Shapley-Shubik指数或Banzhaf指数的多少。把他的体重分散在两个或更多的身份上。对于这两个指数，我们提供了上界和下界的权重分割的效果。然后，我们表明，检查是否存在一个有益的分裂是NP-难的，并讨论了有效的算法限制情况下，这个问题，以及一般情况下的随机算法。我们还提供了这些算法的实验评估。最后，我们研究了相关形式的操纵行为，如兼并，其中一个球员包括其他球员，或合并，其中几个球员联合成一个。我们的特点，这种操纵的计算复杂性，并提供其影响的限制。对于Banzhaf指数，我们描述了一个新的悖论，我们称之为兼并非单调悖论。
英文摘要：
Weighted voting is a classic model of cooperation among agents in decision-making domains. In such games, each player has a weight, and a coalition of players wins the game if its total weight meets or exceeds a given quota. A players power in such games is usually not directly proportional to his weight, and is measured by a power index, the most prominent among which are the Shapley-Shubik index and the Banzhaf index.In this paper, we investigate by how much a player can change his power, as measured by the Shapley-Shubik index or the Banzhaf index, by means of a false-name manipulation, i.e., splitting his weight among two or more identities. For both indices, we provide upper and lower bounds on the effect of weight-splitting. We then show that checking whether a beneficial split exists is NP-hard, and discuss efficient algorithms for restricted cases of this problem, as well as randomized algorithms for the general case. We also provide an experimental evaluation of these algorithms. Finally, we examine related forms of manipulative behavior, such as annexation, where a player subsumes other players, or merging, where several players unite into one. We characterize the computational complexity of such manipulations and provide limits on their effects. For the Banzhaf index, we describe a new paradox, which we term the Annexation Non-monotonicity Paradox.
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