Reference no: EM132197788

Question: 1. (a game played by Nash and his graduate school colleagues as you watched in the movie clip during the class) In the film A Beautiful Mind, John Nash and three of his graduate school colleagues find themselves faced with a dilemma while at a bar. There are four brunettes and a single blonde available for them to approach. Each young man wants to approach and win the attention of one of the young women. The payoffs of each of winning the blonde is 10; the payoff of winning a brunette is 5; the payoff from ending up with no girl is 0. The catch is that, if two or more young men go for the blonde, she rejects all of them and then the brunettes also reject the men because they don't want to be second choice. Thus, each player gets a payoff of 10 only if he is the sole suitor for the blonde.

a) First consider a simpler situation where there are only two young men, instead of four. There are two brunettes and one blonde, but these women merely respond in the manner just described and are not active players in the game. Show the payoff table for the game, and find all of the pure strategy Nash equilibria of the game.

b) Now suppose there are three young men (and three brunettes and one blonde). Find all of the Nash equilibria of the game.

c) Use your results above to generalize your analysis to the case in which there are n young men (and n brunettes and one blonde). Can the outcome specified in the moves as the Nash equilibrium of the game--that all of the young men choose to go for brunettes-ever be a true Nash equilibrium of the game?