论文标题
可分开的游戏
Separable games
论文作者
论文摘要
我们介绍了可分离游戏的概念，相对于向前的指向HyperGraph（FDH-Graph），它可以完善并概括图形游戏的概念。首先，我们表明，游戏是可以分开的最少的FDH图形，为游戏提供了最小的复杂性描述。然后，我们证明了潜在游戏最小的FDH环的对称属性，我们描述了它如何反映在局部功能方面对潜在功能的分解。特别是，这些最后的结果加强了最近证明的图形潜在游戏。最后，我们研究了有限游戏在其谐波和潜在组件中的可分离性与分解之间的相互作用，表征了这两个组件的可分离性能。
We present the notion of separable game with respect to a forward directed hypergraph (FDH-graph), which refines and generalizes that of graphical game. First, we show that there exists a minimal FDH-graph with respect to which a game is separable, providing a minimal complexity description for the game. Then, we prove a symmetry property of the minimal FDH-graph of potential games and we describe how it reflects to a decomposition of the potential function in terms of local functions. In particular, these last results strengthen the ones recently proved for graphical potential games. Finally, we study the interplay between separability and the decomposition of finite games in their harmonic and potential components, characterizing the separability properties of both such components.
