3. 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 . Player 2, the receiver, likes to fight with the sender if he is weak, but doesn't want to fight if he is strong. However, before 2 is making the decision of whether or not to pick a fight, 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 fight. Concretely, suppose that payoffs are additive and that; For the weak type: Beer Quiche Fight 0 Don't 2 For the strong type Beer Quiche Fight Don't NO Finally, the receiver gets the following payoffs Sender Weak Sender Strong Fight Don't OH1. Use the information above to draw the associated extensive form of the signalling game described. . Under what conditions on p, is there is a pooling equilibrium where both players have beer for breakfast. 3. Under what coditions on ,u is there a pooling equilibrium where both players have quiche for breakfast. 4. Under what coditions on p, is there a separating equilibrium? . Is there a range for a without a pure strategy equilibrium? If so, can you construct a mixed strategy equilibrium