Question: Recall the movie clip "A Beautiful Mind" about John Nash that we watched in class. Debating, whether they should go for the blonde in the bar:the Hollywood version of Nash suggests that 'no one should pursue the blonde" should be the outcome.
Suppose you and your buddy were in the scene of the movie. Seeing a blond and two brunettes entering the bar, you both have to make a decision simultaneously out of 2 strategies:to go for the blonde (BL), or to go for a brunette (BR). Assume you study much harder than your friend:whether dating a blond or a brunette, it does not mean as much as it does to your friend. Here is your payoff structure (mental, non-monetary):
- If you go for the blonde, and your friend does as well, neither of you will get the blonde, as you block each other. So the payoff for each of you is zero.
- If you go for the blonde, and your friend goes for a brunette, your payoff is 8, and him 7.
- If you go for a brunette, and your friend goes for the blonde, then your payoff is 5, and your friend 10.
- If both of you go for the brunettes, you get 5, and him 7.
(a) Construct a 2 times 2 payoff matrix for you (player 1) and your friend (player 2).
(b) Do you have a dominant strategy? Why or why not? What is your dominant strategy, if existing?
(c) Does your friend have a dominant strategy? Why or why not? What is his dominant strategy, if existing?