a) Suppose there are only three men in total. This means that you can use payoffmatrices to represent the strategic form: let player 1 choose a row, player 2 choose a column,and player 3 choose a matrix. Write the payoff matrices and find all the Nash equilibria.

(b) Suppose now there arenmen in total (and there is one blonde and at leastnbrunettein the Bar), wheren >5. Is the strategy profile everyone chooses BL a Nash equilibrium?Is there a Nash equilibrium in which at least two men choose BL? Find all the Nash equilibria.

The Bar Scene in A Beautiful Mind Rule of the game: If a player chooses BR, he will be accepted, and hence gets 5. If a player chooses BL, he will get 10, if no one else chooses BL, 0, if at least one of the others choose BL. Question: game: Is Nash's suggestion everyone chooses BR a Nash equilibrium? Is the strategy profile Nash chooses BL, everyone else chooses BR a Nash equilibrium? Are there other Nash equilibria? s "everyone chooses BR a Nash equilibrium (NE)? We check whether every player is content to BR. Let's look at Nash first. Given everyone else chooses BR, If Nash chooses BR, he gets . If Nash chooses BL, he gets , since he will be the only one who chooses BL. So, Nash is not content to BR, that is, he is not playing a best reply to the other players' strategies. We can conclude that everyone chooses BR is not a NE. Are there other NE? We have shown that (BL, BR, BR, BR, BR) is a NE (the first strategy refers to Nash's strategy, and the last four strategies refer to friend 1, 2, 3, and 4 strategy.) . Since the game is symmetric, the following are also NE, (BR, BL, BR, BR, BR) (BR, BR, BL, BR, BR) (BR, BR, BR, BL, BR) (BR, BR, BR, BR, BL) Are there her NE Consider a strategy profile in which two players choose BL. Is it a NE? The Bar Scene in A Beautiful Mind Rule of the game: If a player chooses BR, he will be accepted, and hence gets 5. If a player chooses BL, he will get 10, if no one else chooses BL, 0, if at least one of the others choose BL. Question: game: Is Nash's suggestion everyone chooses BR a Nash equilibrium? Is the strategy profile Nash chooses BL, everyone else chooses BR a Nash equilibrium? Are there other Nash equilibria? s "everyone chooses BR a Nash equilibrium (NE)? We check whether every player is content to BR. Let's look at Nash first. Given everyone else chooses BR, If Nash chooses BR, he gets . If Nash chooses BL, he gets , since he will be the only one who chooses BL. So, Nash is not content to BR, that is, he is not playing a best reply to the other players' strategies. We can conclude that everyone chooses BR is not a NE. Are there other NE? We have shown that (BL, BR, BR, BR, BR) is a NE (the first strategy refers to Nash's strategy, and the last four strategies refer to friend 1, 2, 3, and 4 strategy.) . Since the game is symmetric, the following are also NE, (BR, BL, BR, BR, BR) (BR, BR, BL, BR, BR) (BR, BR, BR, BL, BR) (BR, BR, BR, BR, BL) Are there her NE Consider a strategy profile in which two players choose BL. Is it a NE