Dad plans to take the two children Bart and Cassie on an outing. Bart prefers Disneyland (D), but Cassie prefers the Modern Art Gallery (M). Each child gets 3 units by going to the more preferred place and 2 units by going to the less preferred place. Dad gets 2 units from either activity.
To choose where to go, Dad will first ask Bart for his choice. Bart will announce one of the two places with Cassie listening. Then Dad will ask Cassie for her choice, and she'll announce one of the two places. If the children make the same choice then the game ends - all three will go there. If the children make different choices, then Dad can choose D or M or he can choose his own favorite, the Encino Galleria (E). He gets 3 from E and both children get 1 from it.
A final rule is this: if the two children make the same choice, then Dad gets 2 extra units, no matter which choice it is.
(a) Draw the tree, and include the payoffs. Compared to the trees we took in class, each endpoint will have three payoffs. So, just making up some numbers, the payoff set 9, 6, 7 at an endpoint means that Bart gets 9, Cassie gets 6 and Dad gets 7.