Simple games and weighted games: A theoretical and computational viewpoint

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• 作者：Josep Freixas ; Xavier Molinero
• 关键词：Hypergraphs ; Simple games ; Asummability ; Trade robustness ; Invariant-trade robustness
• 刊名：Discrete Applied Mathematics
• 出版年：2009
• 出版时间：6 April 2009
• 年：2009
• 卷：157
• 期：7
• 页码：1496-1508
• 全文大小：695 K

文摘

It is a well-known result in the theory of simple games that a game is weighted if and only if it is trade robust. In this paper we propose a variant of trade robustness, that we call invariant-trade robustness, which is enough to determine whether a simple game is weighted. To test whether a simple game is invariant-trade robust we do not need to consider all winning coalitions; a reduced subset of minimal winning coalitions is enough.

We make a comparison between the two methods (trade robustness and invariant-trade robustness) to check whether a simple game is weighted. We also provide by means of algorithms a full classification using both methods, for simple games with less than 8 voters according to the maximum level of (invariant-)trade robustness they achieve.