Economics question

Two players bargain to divide a pie of size 1 and take turns making offers, possibly indenitely. They each discount the future at rate 6. In every period, the player whose turn it is to make the offer makes an offer over how to split the pie. The other player then has a choice between (i) accepting the offer, (ii) leaving the negotiation and taking an outside option 1130 instead, and (iii) remaining at the bargaining table and making a counteroffer in the next period. (a) Show that if 1130 g 6 / (1 + 6) then the outside option has no effect on the equi librium path. (b) What happens to equilibrium bargaining outcomes if :60 > 6 / (1 + 6)? (c) Now suppose that outside options form part of the bargaining process in the following di'erent way: instead of players being able to choose whether to take an outside option, at every period t, bargaining breaks down with exogenous probability (17r) if the periodt offer is turned down. If bargaining breaks down, the game ends and each player obtains the outside option $0. How does this exogenous possibility of breakdown in bargaining affect bargaining outcomes