Chapter+3

Chapter 3: Bargaining
There is only one exercise and it's a modification of the alternating offers bargaining game over $100, where one on the players have an outside option of $50 (i.e. he can leave the game at any point, getting 50 while the other get nothing). My understanding of the game is illustrated in the tree below So, in the first move Bernie wants to offer X0<50 (ideally 1p). How to make sure Ernie accepts? In the second move, if it ever happened, Ernie would better offer d100-X1=d50 so that he gets something. So X1=d50. Going back to the first move, Bernie knows that if he offers Ernie d50 he'll gladly accept, so Bernie manages to keep 100-d50 which is more than the 50 he'd get by leaving the game in the first move. In the original game Bernie would get 100/(1+d) and Ernie 100d/(1+d).