Question

You are deciding about whether you should bring an umbrella today. The value of an
umbrella depends on the weather, which can be (i) either rainy or runny and (ii) either
windy or calm.
• If you bring an umbrella it costs you 5 payoff. • Getting wet costs you 10 payoff • Breaking your umbrella costs you 15 payoff
Which outcome occurs depends on the weather.
• If it rains and you bring your umbrella, you stay dry, otherwise you get wet. • If it’s windy and rainy, and you bring your umbrella it breaks (but you stay dry)
It is windy 25% of the time, and rainy 50% of the time (independently).
(a) (5 points) Draw this as a game tree, where nature makes two moves. (b) (5 points) What if your best response? Explain. (c) (5 points) Now, draw this as a tree where nature makes one move only, and repeat
(b). What is the difference, if any?

Answer 1

a)

b) The best response to nature's any move is not to take an umbrella

Infact my loss will be minimum if I dont take an umbrella assuming Nature is going to play twice.

c)

There is basically no difference when the move of nature is sunny or Windy, however for rainy taking the umbrella is better as the loss is less.