Possessive: Game ball vs Game's ball vs Ball of the game

I don’t know what’s the difference or when I have to use:
game ball
game’s ball
ball of the game

I really want a very clear answer, please.

It’s impossible to answer your question without context for the expressions. None of those expressions are commonly used, so we need you to show us what contexts you saw them in.

OK. And if I am speaking about a soccer game and the ball was lost. How can I reference thar ball?