3 Real Men Don't Eat Quiche (neither do wimps. . .) A man walks into a diner, we'll call him Al, to order breakfast and in this particular diner there are only two possible meals; beer and quiche. There is another man already in the diner who likes to harass others, we'll call him Bert. After seeing Al order his breakfast, Bert decides whether or not to bully him. Since Bert has never seen Al before he doesn't know what kind of person he is. Al could be a tough guy or he could be a wimp and he assumes that nature selected him as being one type or the other before Al walks in the diner such that with probability 1*, Al is a wimp. If Al is tough he prefers beer for breakfast and gets a payoff of 3 if Bert doesn't annoy him. If Al is tough and he orders quiche, well, he eats it but only gets a payoff of 2 assuming Bert doesn't try to bully him. In either case, if Bert tries to bully him, Al's payoff goes down by 1 from the base level. If Al is a wimp, then he prefers quiche for breakfast and gets a payoff of 3 from it if he is not bullied and a payoff of 2 if he orders beer and isn't bullied. Since he is a bit of a wimp, if Bert tries to bully him, his payoff drops by 2 in either case. Bert gets a payoff of 1 from bullying a wimp, 0 from deferring to one. If Bert tries to Bully a tough guy, he gets beaten to a pulp and therefore gets a payoff of -1 whereas if he defers to a tough guy, he gets a payoff of 1. a. Derive the extensive form of this game. b. Find a pooling Bayesian Nash equilibrium of this game assuming that 1' = %. (The title of the question should be taken as a hint) c. For what values of 1' can you not nd a pooling BNE