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16.3 Beeror Quiche? Cho and Kneps { l 98?} introduced what is now a famous two- player signaling game. First. Nature selects player I. who knows his type. to be either a wimp (W). with probability p = U. I. or surly {S}. with probability 1 - p = 0.9. Player 1 then chooses what to have for breakfast: beer {B} or quiche (Q). A surly type prefers beer while a wimp prefers quiche. Player 1's preferred breakfast gives him a payoff of I while his lesspreferred choice gives him D. After breakfast player 2 observes what player I ate but does not know whether he is a wimp or surly. Player 2 then [:th whether to duel {D} with player I or not to duel {N}. Player 1, regardless of his type. prefers no duel, yielding him an extra payoff of 2. to a duel, which gives him fl. {For example. if player I eats his preferred breakfast and avoids a duct then his nal payoff is 3. while if he eats his preferred breakfast and is forced into a duel then his nal payoff is 1.} Player 2. however. prefers to duel if and only if player 1 is a wimp. If player I is surly then player 2's payoff is II} from D and I from N. lt'player l is a wimp then player 2's payoff is 2 from D and I from N. a. Draw the extensive form of this game. b. What are the Bayesian Nash equilibria of this game? e. 1What are the perfect Bayesian equilibria'? d. thhe equilibria you found in (c). which fail the intuitive criterion