Strategic thinking

Father of Alice and Bob has $10. The father is a game theorist and wants to teach them how to share. The father is willing to let Alice and Bob have the $10, but only according to the following procedure: Alice and Bob are each to submit a written request as to their share of the $10 without seeing the other's request. Let a 6 [0,10] denote the amount that Alice requests for herself and b E [01 10] be the amount that Bob requests for himself. If the aggregate amount a + b is less than or equal to 10, then the two receive what they requested, and the remainder, 10 7 a. 7 b, is split equally between them. If, however, they are too selfish and hence the aggregate amount alb > 10, then they get nothing, and the father keeps the 5510. Alice and Bob are the players in this game (Father is not a player, he is just a mediator). Assume that each of Alice and Bob has a payoff equal to the amount of money that he or she receives. Find all pure strategy Nash equilibria. [You can draw best response curves if you find them useful.]