There are two players, A and B. Each player i 6 {A, B) can be of one of two types & C {1, 2). The probability that a player is of type 2 equals ,. When A and B meet, each can decide to fight or cave. If both players fight, then player i gets payoff ti + ty -cjfi where c > 0. If player : fights, but player j does not, then player i gets payoff 1, while player j gets payoff 0. If both players do not fight, each gets payoff 1/2. 1.1 Draw the Bayesian normal form representation of this game . 1.2 Recall that 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. 1.3 Assume that A plays fight if ta = 2 and cave otherwise. If B is of type 2, what should she do? If she is of type 1, what should she do? 1.4 Is there a Bayesian Nash equilibrium in which each player fights if and only if she is of type 2? If so, what is the equilibrium probability of a fight? 1.5 Assume that A never fights. If B is of type 2, what should she do? If she is of type 1, what should she do? 1.6 Is there a Bayesian Nash equilibrium in which no player ever fights