The beer-quiche game. a group of sorority sisters from "delta house" is in a restaurant in ogden. some of the sisters are weak and some of them are strong. there is a group of sisters from a competing sorority, "gamma house," outside on the sidewalk. the sisters from gamma house will fight a sister from delta house if they believe she is weak, and will praise, a sister from delta house if they believe she is strong, because they will lose a fight against a strong sister, but will win a fight against a weak sister. a sister from delta house will get payoff w if they win a fight against gamma house, will get payoff l if they lose a fight against gamma house, and will get payoff p if they are praised with w > p > l.
the delta sisters can order either quiche or beer from the restaurant. the benefit-cost associated with consuming quiche is bcq, while the benefit-cost associated with consuming beer is bcb. assume that bcb is the same for all delta sisters, and that bcq is the same for all delta sisters, but bcb does not equal bcq. further, the gamma sisters will believe that a consumer of quiche is weak, and a consumer of beer is strong. (clue: write out the 4 possible payoff outcomes for delta sisters - 2 types x 2 possible actions - to answer the following questions.)

show the payoff ordering(s), in simplest possible terms (fewest necessary variables), that would lead to the two different possible pooling equilibriums: all delta sisters order quiche, or all delta sisters order beer. also, write a sentence describing the preference ordering(s) in words.
show the payoff ordering(s) that would lead to a separating equilibrium in which all weak delta sisters order beer, and all strong delta sisters order quiche. also, write a sentence describing the preference ordering(s) in words.
show that the delta sisters will never all reveal their true type under these payoff assumptions.