An example from last month, I had a haircut at a new place and the guy refused to tell me how much I should pay him and insisted its on him this time, I know he's bluffing but he kept doing it. So I just guessed and gave him the money which he pretended he didn't want for the last 5 minutes, he immediately realized it was less than he wanted and asked for more!
This confusing and conflicting behavior should stay far away from any attempt to develop a standard linguistic approach to communication which I hope LLMs are aiming to achieve.
If I was chaotic neutral, I'd totally play along with their bluffing and watch them get really confused.