That explains why player 1 should not offer only $1, but it doesn't explain why player 2 would not take $1 if offered. If there is no chance of renegotiation, a

That explains why player 1 should not offer only $1, but it doesn't explain why player 2 would not take $1 if offered. If there is no chance of renegotiation, and you already got an offer of free money, it is irrational to not take the money. The only reason player 2 would do so is if: (1) this is a regularly occuring event and they want to help future player 2s, or (2) they like the emotional response of spiting player 1.