Consider a father who is trying to discipline his child. The father insists that the child must go with the rest of the family to visit their grandmother. The child prefers to go to the movies with a friend. The father threatens to punish the child if the child doesn't visit the grandmother. If the child goes with the family to visit the grandmother, both the child and the father receive one unit of utility. If the child refuses to go to the grandmother's house, and the father punishes the child, the child receives one unit of utility, and the father receives one unit of utility. If the child refuses to go and the father relents (does not punish), the child receives two units of utility, and the father receives none.
a. Draw this game in matrix form.
b. Draw this game in extensive form.
c. Solve this game via backward induction.