Specifically , the game 's core is non-empty if and only if the game is balanced .
The Bondareva -- Shapley theorem , in game theory , describes a necessary and sufficient condition for the non-emptiness of the core of a cooperative game in characteristic function form .
The game 's core is non-empty if and only if the game is balanced .
The Bondareva -- Shapley theorem , in game theory , describes a necessary and sufficient condition for the non-emptiness of the core of a cooperative game in characteristic function form .