Question

Bill and Ted are deciding what musical instruments they want to learn pick between the guitar, keyboard, and the drums to play for their band. They can They both want to have a good band, but also each has a preference over what to play. Both like the guitar over all else. However, Bill likes the keyboard more than the drums and Ted likes the drums 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 and learned to play. Since they bought AND learned to play the instru- are committed to it! Given the information above, answer the following: ment they

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 exist a 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

Answer and Explanation:

1. There is no dominant strategy as each person has to respond with a different strategy like using a different instrument depending on the instrument chosen by the other to achieve best payoff

2. If Bill picks keyboard then it would be best for Ted to pick guitar as this is his preferred instrument which would bring best payoff

3. If Ted picks guitar, then bull should pick keyboard which he prefers and would be the best payoff

4. A nash equilibrium would not exist here since Ted should choose guitar if bull chooses drums and bill should choose guitar if Ted chooses keyboard

5. A Nash equilibrium can exist here since Ted should choose drums when bill chooses guitar.