Question

Bill and Ted are deciding what musical instruments they want to learn to play for their band. They can pick between the guitar, keyboard, and the drums.They both want to have a good band, but also each has a preference over what toplay. Both like the drums over all else. However, Bill likes the keyboard more thanthe guitar and Ted likes the guitar more than the keyboard. What is crucial is that each chooses a different instrument, otherwise the band is pretty terrible. The actual combination does not affect the quality of the band. One night, Bill and Ted simultaneously reveal to each other what instrument they have bought decided to learn. Since they bought the instrument they are committedto learning it! Given the information above,

1. Does either Bill or Ted have a dominant/dominated strategy? Explain.
2. If Bill picks the keyboard, is it a best response for Ted to pick the drums? Explain.
3. If Ted picks the guitar, is it a best response for Bill to pick the keyboard? Explain.
4. Can there exista Nash equilibrium in which Bill picks the drums and Ted picks the keyboard? Explain.
5. Can there exist a Nash Equlibrium in which Bill picks the guitar and Ted picks the drums? Explain.

Answer 1

1. Does either Bill or Ted have a dominant/dominated strategy? Explain.

No, since both like playing the drums. But if both choose the drums, then there is no band.

2. If Bill picks the keyboard, is it a best response for Ted to pick the drums? Explain.

yes, since Ted likes the drums more than the guitar.

3. If Ted picks the guitar, is it a best response for Bill to pick the keyboard? Explain.

No, Bill should pick the drums since he likes them more.

4. Can there exist a Nash equilibrium in which Bill picks the drums and Ted picks the keyboard? Explain.

No, because they both prefer the drums, but Ted doesn't like the keyboard.

5. Can there exist a Nash Equilibrium in which Bill picks the guitar and Ted picks the drums? Explain.

No, because they both prefer the drums, but Bill doesn't like the guitar.