2. (25 pts) Consider the following dynamic game of incomplete information. At time 0 \"nature\" draws the type of player 1 (the sender), which may be \"strong\" or \"weak\" , where the probability of a strong sender is a. Player 2, the receiver, likes to ght with the sender if he is weak, but doesn't want to ght if he is strong. However, before 2 is making the decision of whether or not to pick a ght, player 1 can have one of two possible breakfasts: either he starts his day with a pitcher of beer, or he may have a quiche. The \"strong\" type likes beer and the \"weak\" type likes quiche. However, both would like to avoid a ght. Concretely, suppose that payoffs are additive and that; For the weak type: Beer Quiche Fight 0 2 Don't 3 5 For the strong type Beer Quiche Fight 2 0 Don't 5 3 Finally, the receiver gets the following payoffs Sender Weak Sender Strong Fight 2 0 Don't 0 1 1. (5 pts) Use the information above to draw the associated extensive form of the signalling game described. 2. (5 pts) Under what conditions on a is there is a pooling equilibrium where both players have beer for breakfast. 3. (5 pts) Under what conditions on ,u, is there a pooling equilibrium where both players have quiche for breakfast. 4. (5 pts) Under what conditions on a is there a separating equilibrium? 5. (5 pts) Is there a range for ,u without a pure strategy equilibrium? If so, can you construct a mixed strategy equilibrium