The Beer-Quiche Game. A group of sorority sisters from "Delta House" is in a restaurant in Ogden. Some of the sisters are Weakand 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 Fighta 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 Wif they win a fight against Gamma House, will get payoff L if they lose a fight against Gamma House, and will get payoff Pif they are praised with W > P > L.

The Delta sisters can order either Quicheor Beerfrom the restaurant. The benefit-cost associated with consuming Quicheis BC_Q, while the benefit-cost associated with consuming Beeris BC_B. Assume that BC_B is the same for all Delta sisters, and that BC_Q is the same for all Delta sisters, but BC_B does not equal BC_Q. Further, the Gamma sisters will believe that a consumer of Quicheis Weak, and a consumer of Beeris Strong. (Clue: Write out the 4 possible payoff outcomes for Delta sisters - 2 Types x 2 Possible Actions - to answer the following questions.)

1. 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.

2. Show the payoff ordering(s) that would lead to a separating equilibrium in which all WeakDelta sisters order Beer, and all StrongDelta sisters order Quiche. Also, write a sentence describing the preference ordering(s) in words.

3. Show that the Delta sisters will never all reveal their true type under these payoff assumptions.