关于k-可加核的顶点
On the vertices of the k-addiive core
摘要：
$N$上的博弈$v$的核心，是一组加性博弈$ϕ$支配$v$使得$ϕ(N)=v(N)$，是合作博弈论、决策和组合学中的中心概念，它与子模函数、拟阵和贪心算法有关。然而，在许多情况下，核心是空的，必须找到替代的解决方案。我们定义了$k$ -可加核心，通过在核心的定义中用$k$ -可加游戏替换可加游戏，其中$k$ -可加游戏是那些莫比乌斯变换对于多于$k$元素的子集为零的游戏。对于足够高的$k$值，$k$可加核是非空的，并且是凸闭多面体。我们的目标是建立类似的经典结果Shapley和Ichiishi的凸对策的核心（对应于埃德蒙兹定理的贪心算法），它的特点的核心的顶点。
英文摘要：
The core of a game $v$ on $N$, which is the set of additive games $ϕ$ dominating $v$ such that $ϕ(N)=v(N)$, is a central notion in cooperative game theory, decision making and in combinatorics, where it is related to submodular functions, matroids and the greedy algorithm. In many cases however, the core is empty, and alternative solutions have to be found. We define the $k$-additive core by replacing additive games by $k$-additive games in the definition of the core, where $k$-additive games are those games whose Möbius transform vanishes for subsets of more than $k$ elements. For a sufficiently high value of $k$, the $k$-additive core is nonempty, and is a convex closed polyhedron. Our aim is to establish results similar to the classical results of Shapley and Ichiishi on the core of convex games (corresponds to Edmonds' theorem for the greedy algorithm), which characterize the vertices of the core.
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