Problem
To give Mom and day of rest, Dad plans to take their two children, Aiden and Isabella, on an outing on Sunday. Isabella prefers to go to the amusement park (A), whereas Aiden prefers to go the science museum (S). Each child gets 3 units of gain from her/his more preferred activity, and only 2 units of gain from her/his less preferred activity. Dad gets 2 units of gain from either activity.
To choose their activity, Dad plans first to ask Isabella for her preference, then to ask Aiden after he hears Isabella's choice. If both children choose the same activity, then that is what they will do. If the children choose different activities, Dad will make a tie breaking decision. Dad though has an additional option: he can choose the amusement park, the science museum, or his personal favorite, the mountain hike (M). Aiden and Isabella each get 1 unit of gain from the mountain hike, and Dad gets 3 units of gain from the mountain hike.
Because Dad wants his children to cooperate with one another, he gets 2 units of extra gain if the children choose the same activity (no matter what it is).
A. Draw the game tree.
B. What is the equilibrium? Explain your reasoning and prune the tree when you are explaining how you find equilibrium.
C. Is there a first mover advantage in the game? Explain.
D. If there is a first mover advantage, what is the source of this advantage? Explain.
E. Explain what you understand by the following assertion (tell a story): the children will behave the way we would predict based on our equilibrium outcome if the father's threat is credible. In your explanation address two questions: What is the threat and what does it mean to say that it is credible?