Question

Two players, A and B, have $1 to divide between them. They agree to spend at most three days negotiating over the division. If they can’t come to an agreement they both get nothing, i.e. $0. The first day, A will make an offer, B either accepts or comes backs with a counteroffer the next day, and on the third day A gets to make one final offer if he rejected the offer of B on day 2. Both A and B differ in their degree of impatience. A discounts payoffs in the future at a rate of ? per day, i.e. $1 tomorrow is worth $? today to A. In the case of B, he discounts the future payoffs at a rate of ? per day. Assume that if a player is indifferent between two offers, he will accept the one most preferred by the other player. Find the unique subgame perfect Nash equilibrium.

a) What happens when ? = 1??

b) Would your answer change if the game had a duration of two days and that B was the first to make an offer? What do you infer from this?

Answer 1