HiThey may not accept the highest offer because they want more...

Hi

They may not accept the highest offer because they want more than that, whether realistic or not.

Yes, it is a game. Personally, I would make the offer and tell the agent they can get back to me if they want to and leave it at that. The mere act of you chasing them up shows interest from your side which tells them more than you want them to know.

all the best