find all of the Nash equilibria of the game. (c) Use your results to parts a and b to generalize your analysis to the case in which there are four you ng men and then to the case in which there is some arbitrary number

12. In the film A Beautiful Mind, John Nash and three of his grad uate 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 payoff to each of winning the blonde is 10; the payoff of win­ ning 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 rejec t 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 con ider a simpler situation where there are only two young men, instead of fou r. (There are two brunettes and one blonde, but these women m rel. respond in the manner just described and are not active player in rhe game.) Show the playoff table for the game, and find all of the pu re-strategy Nash equilibria of the game. (bl :”o\’ how the (three-dimensional) table for the case in which there are three young men (and three brunettes and one blonde who are not ac­ [ive players). Again