We introduce the notion of separable games, which refines and generalizes that of graphical games. We prove that there exists a minimal splitting with respect to which a game is separable. Moreover we prove that in every strategic equivalence class, there is a game separable with respect to the minimal splitting in the class. This game is also graphical with respect to the smallest graph in the class, which represent a minimal complexity graphical description for the game. We prove a symmetry property of the minimal splitting of potential games and we describe how this property reflects to a decomposition of the potential function. In particular, these last results strengthen the ones recently proved for graphical potential games. Finally, we study the interplay between separability and the classical decomposition of games proposed by [5], characterizing the separability properties of each part of the decomposition.

中文翻译：

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可分离的游戏

我们介绍了可分离游戏的概念，它改进和概括了图形游戏的概念。我们证明存在关于博弈可分的最小分裂。此外，我们证明，在每个策略等价类中，存在一个关于类中最小分裂的博弈可分。这个游戏也是关于类中最小图形的图形，它代表游戏的最小复杂性图形描述。我们证明了潜在博弈最小分裂的对称性，并描述了这个性质如何反映到潜在函数的分解中。特别是，这些最后的结果加强了最近在图形潜在游戏中证明的结果。最后，我们研究了 [5] 提出的可分离性和经典游戏分解之间的相互作用，