论文标题
$ \ tilde {\ Mathcal {p}} _ {\ min} $的凸的继承
Inheritance of Convexity for the $\tilde{\mathcal{P}}_{\min}$-Restricted Game
论文作者
论文摘要
我们考虑在与最小分区相关的加权图上进行限制的游戏。我们在Myerson限制游戏的经典定义中替换了用特定分区$ \ tilde {\ Mathcal {p}} _ {\ min} $获得的子组件的连接组件。该分区依赖于与分区$ \ Mathcal {p} _ {\ min} $相同的原理，该份子由Grabisch and Skoda（2012）引入，但仅限于连接的联盟。更准确地说，此新分区$ \ tilde {\ Mathcal {p}} _ {\ min} $是由与联盟关联的每个连接组件中的最小重量边缘的删除诱导的。我们提供了满足从基础游戏到与$ \ tilde {\ Mathcal {p}} _ {\ min} $相关的限制游戏的凸的继承的图表的表征。
We consider a restricted game on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the sub-components obtained with a specific partition $\tilde{\mathcal{P}}_{\min}$. This partition relies on the same principle as the partition $\mathcal{P}_{\min}$ introduced by Grabisch and Skoda (2012) but restricted to connected coalitions. More precisely, this new partition $\tilde{\mathcal{P}}_{\min}$ is induced by the deletion of the minimum weight edges in each connected component associated with a coalition. We provide a characterization of the graphs satisfying inheritance of convexity from the underlying game to the restricted game associated with $\tilde{\mathcal{P}}_{\min}$.
