Exercise 2. While this question has similarity with exercise 1, please treat this as an independent ques- tion. Like the last part of Exercise 1, this one is also about incomplete information. However, here, not only A does not know about B's type, but also B does not know about A's type. This is an example of two-sided private information. There are two players, A and B. Each player i c {A, B) can be of one of two types: The probability that a player is of type 2 equals p. When A and B meet, each can decide to fight or cave. If both players fight, then player i gets payoff - c litt; where j # i and c20. Rest of the payoffs are the same as in Exercise 1. (a) (1 mark) Draw the Bayesian normal form representation of this game. [Hint: draw one payoff matrix] (b) (1 mark) A strategy in a static Bayesian game is a function that specifies an action for each type of a player. Write down all the possible strategies for player i. [Hint: each player has four strategies] (c)(2 marks) Assume that A plays fight if A = 2 and cave otherwise. (i) If B is of type 2, what should B do? (ii) If B is of type 1, what should B do? (d) (2 marks) Is there a Bayesian Nash equilibrium in which each player fights if and only if she is of type 27 If so, what is the equilibrium probability of a fight? [Note: Fight occurs in equilibrium when both player chooses to fight] (e) (2 marks) Assume that A never fights. (i) If B is of type 2, what should B do? (ii) If B is of type 1, what should B do? (f) (2 marks) Is there a Bayesian Nash equilibrium in which no player ever fights