To give Mom a day of rest, Dad plans to take his two children, Bart and Cassie,
ID: 1168739 • Letter: T
Question
To give Mom a day of rest, Dad plans to take his two children, Bart
and Cassie, on an outing on Sunday. Bart prefers to go to the amusement
park (A), whereas Cassie prefers to go to the science museum (S). Each child
gets 3 units of utility from his/her more preferred activity, and only 2 units
of utility from his/her less preferred activity. Dad gets 2 units of utility for
either of the two activities. To choose their activity, Dad plans rst to ask
Bart for his preference, then to ask Cassie after she hears Bart's choice. Each
child can choose either the amusement park (A) or the science museum (S).
If both children choose the same activity, then that is what they will all
do. If the children choose dierent activities, Dad will make a tie-breaking
decision. As the parent, Dad has an additional option: he can choose the
amusement park, the science museum, or his personal favorite, the mountain hike (M). Bart and Cassie each get 1 unit of utility from the mountain hike,
and Dad gets 3 units of utility from the mountain hike. Because Dad wants
his children to cooperate with one another, he gets 2 extra units of utility if
the children choose the same activity (no matter which one of the two it is).
a) Draw the game tree, with payos, for this three-person game.
b) What is the rollback equilibrium to this game? Make sure to describe
the strategies, not just the payos.
c) How many dierent complete strategies does Bart have? Explain.
d) How many complete strategies does Cassie have? Explain.
Explanation / Answer
Casie DAD
Bart ---- A --------A ------(3,2,4)
--------S---------A----(3,2,2)
--------S----(2,3,2)
-------M---(1,1,3)
------ S-------S-------(2,3,4)
-------A --------A----(3,2,2)
--------S----(2,3,2)
-------M---(1,1,3)
b) Roll back equilibrium to this game is both bart and cassie is both bart and cassie plays A.
c) Bart has 2 strategies. i.e A or S
d) Cassie has 4 strategies : AS, SS, SA, AA
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