are you allowed to play with fake money on Shabbos like monopoly game and alike ?
Yes, there is no prohibition of playing with fake money. However, for adults this type of recreation is certainly not in the spirit of Shabbos.
The Rama in 338:5 speaks of a type of gambling game where one wins from the other, which is a form of prohibited transaction on Shabbos [Monopoly is not this type of game, as no one wins ownership of anything]. Even that game the Rama writes not to stop children from playing as they will not listen anyway, and better they be unaware of the prohibition.