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 .
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 .
R
introduce
present
R
games
game with respect to a forward directed hypergraph (FDH-graph)
R
games. We prove
game. First, we show
R
splitting
FDH-graph
R
. 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
, providing a minimal complexity
R
We
Then, we
R
splitting
FDH-graph
R
this property
it
A
in terms of local functions
D
classical decomposition of games proposed by
R
5
decomposition of finite games in their harmonic and potential components
R
each part of the decomposition
both such components