Consider a situation that there are two persons, A and B, who bargains over a cake of size one. If they agree on how to allocate the cake between them, then they can enjoy the allocation of the cake. If they cannot agree on it, then both of them receive only 0.1 share of the cake as the disagreement allocation. If x [0,1] is allocated to player i = A,B, then i can enjoy the payoff ui (x) = x for i = A,B.

Given this bargaining problem, answer the following questions:

(1) If they make this bargaining by following the Ultimatum Bargaining rule, what will be the subgame perfect equilibrium of this Ultimatum Bargaining game? Moreover, specify the subgame perfect equilibrium payoff allocation of this game.

(2) If they make this bargaining by following the cooperative bargaining ap- proach, what will be the payoff allocation recommended by the Nash bargaining solution?