If your offer was genuine and had been calculated on a reasonable basis I would just hold firm and let the agent play their games. The more you get involved you tend to lose your bargaining power. You have made an offer and it is up to them to reject or accept and then go from there.
As for other parties being allegedly involved, maybe or maybe not, you will never know.
Always many properties out there to look at and acquire, have a game plan and stick to it, don't play their game cause they have the advantage.
