4. Consider the following normal-form games: L R U 1, -1 -1, 1 1 D -1,1 1,-1 L R U 1,1 -1, -1 1 D -1,1 1, -1 The intended interpretation is that player 2 has two possible types, and to- When player 2 is of type , both players play the game on top. Instead, when player 2 is of typet, then they play the game on the bottom. Nature informs player 2 of her type but not to player 1. Hence, player 1 is never informed what's the game they play. Suppose that each type of player 2 occurs with probability 1/2. a. What are the pure strategies of these players? b. What pure strategies are interim dominated? For what types? c. Draw the normal-form of the expanded game and find all the pure BNE