S and J are trying to split 100 dollars. In bargaining round 1, S makes an offer at cost 0, proposing to keep S1 for himself and J either accepts (ending the game) or rejects. In round 2, J makes an offer at cost 10 of S2 for S and S either accepts or rejects. In round 3, S makes an offer of S3 at cost c, and J either accepts or rejects. If no offer is ever accepted, the 100 dollars goes to a third player, D.
a) if c=0, what is the equilibrium outcome? what if c=80? c=10?
b) what happens if c=0, but Jones is very emotional and would spit S's face and throw the 100 dollars to D if S proposes S=100? Assume here that S knows J's personality perfectly.