You are in love with a beautiful girl. There is some chance that she likes jewelry (LJ) and some independent chance that she loves flowers (LF). If she is a girl from the city (C), it is quite likely that she likes jewelry (P(LJIC) = 0.7) and not so likely that she likes flowers (P(LF|C) = 0.5). Otherwise, it is the other way around. You are trying to decide on a birthday gift for her. Your possible actions are to buy flowers (F) or a diamond ring (R). Unfortunately, you don't have the money to buy both. We measure your sadness about the loss of money in utility. You decide that buying flowers has a cost of 50 utility, buying the diamond ring has a cost of 500 utility. Depending on her preferences, her happiness (H) about your gift will be different. The following table gives an overview about the utility that you get from her happiness, depending on your decision and her preferences. It does not include the price of the gift. LJ LF A H 350 100 500 50 500 f 1000 t 50 f 0 t t t f F F F F R R R R f f a) (3 Points) Draw the Decision Network for this problem. You assume that 65% of girls live in cities. You may ignore the utility price of the gift in task a) if you want. b) (5 Points) Assuming she is a city girl, what is the expected value of buying flowers and what is the expected value of buying the ring? c) (6 Points) Assuming she is a city girl and you are a rational agent, how much would you be willing to pay to know if she likes jewelry? Hint: If she likes jewelry, the best action is buying the ring, if she does not, the best action is buying flowers. You are in love with a beautiful girl. There is some chance that she likes jewelry (LJ) and some independent chance that she loves flowers (LF). If she is a girl from the city (C), it is quite likely that she likes jewelry (P(LJIC) = 0.7) and not so likely that she likes flowers (P(LF|C) = 0.5). Otherwise, it is the other way around. You are trying to decide on a birthday gift for her. Your possible actions are to buy flowers (F) or a diamond ring (R). Unfortunately, you don't have the money to buy both. We measure your sadness about the loss of money in utility. You decide that buying flowers has a cost of 50 utility, buying the diamond ring has a cost of 500 utility. Depending on her preferences, her happiness (H) about your gift will be different. The following table gives an overview about the utility that you get from her happiness, depending on your decision and her preferences. It does not include the price of the gift. LJ LF A H 350 100 500 50 500 f 1000 t 50 f 0 t t t f F F F F R R R R f f a) (3 Points) Draw the Decision Network for this problem. You assume that 65% of girls live in cities. You may ignore the utility price of the gift in task a) if you want. b) (5 Points) Assuming she is a city girl, what is the expected value of buying flowers and what is the expected value of buying the ring? c) (6 Points) Assuming she is a city girl and you are a rational agent, how much would you be willing to pay to know if she likes jewelry? Hint: If she likes jewelry, the best action is buying the ring, if she does not, the best action is buying flowers
