论文标题
简单复合物的概率值
Probabilistic values for simplicial complexes
论文作者
论文摘要
在本手稿中，我们在简单复合物上定义和研究合作游戏的概率价值。受Weber“游戏的概率值”的工作的启发，我们按照经典的公理化建立了新的理论，即使用线性公理，虚拟公理，等等。 此外，我们在简单络合物上定义了沙普利的价值，从而在文献中概括了经典概念。值得注意的是，Shapley值的传统公理化可以扩展到此一般设置的相当有趣的综合体，这些综合体概括了顶点传播图和顶点均匀的简单复合物的概念。这些组合物体在文献中非常流行，因为研究了复杂性理论中的逃避性猜想。
In this manuscript, we define and study probabilistic values for cooperative games on simplicial complexes. Inspired by the work of Weber "Probabilistic values for games", we establish the new theory step by step, following the classical axiomatization, i.e. using the linearity axiom, the dummy axiom, etc. Furthermore, we define Shapley values on simplicial complexes generalizing the classical notion in literature. Remarkably, the traditional axiomatization of Shapley values can be extended to this general setting for a rather interesting class of complexes that generalize the notion of vertex-transitive graphs and vertex-homogeneous simplicial complexes. These combinatorial objects are very popular in the literature because of the study of Evasiveness Conjecture in Complexity Theory.
