Consider the following two payoff matrices, in which player 1 is the row player and player 2 is the column player (as usual): L R L R 11 T 1,1 T-- m B m. B 0,4 Matrix A Matrix B Each player has some private information that the other player does not have: a Player 1 knows which of the matrices represent the players' actual payoffs, but player 2 only knows that Nature chooses Matrix A with probability 1/2 and Matrix B with probability 1/2. 0 Player 2 knows the true value of a: (which is either equal to 3 or 1) but player 1 only knows that Nature chooses a: = 3 with probability 1/ 2 and a: = 1 with probability 1 / 2. Nature chooses which game the players are playing and the true value of :2: independently from each other. 1. Write down the list of available strategies for both players. 2. Write down the incomplete information game in the normal form using one payoff matrix containing expected payoffs for both players. 3. Find all pure strategy (Bayesian) Nash equilibria of the game