"I will stand firm on A until A becomes worth less than C is now, then I will accept B or C. You get more by accepting B or C now than you get by trying to get more."

One rational course of action is to mutually commit to a random split, and follow through. What's the rational course of action to respond to someone who makes that threat and is believed to follow through on it? If it is known that the other two participants are rational, why isn't making a threat of that nature rational?