The rotten kid theorem. A child's action generates income ()for her and ()for her parents. The child cares only about her own income level. The parents love the child so much that their utility is determined by the smaller of their income and their child's income; in order to maximize their utility, they can give money to (or take money from) the child after the child's choice of is revealed. We model this game with the child choosing in the first stage and then the parents determining how much income they will give to the child.

a)Find the subgame perfect Nash equilibrium and comment on the solution.