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[16 points] First, consider the following game in strategic fonn for two players. L R Player 2's action U (6,6) (1,7) D (7,1) (0,0) Player 1's action As usual, the first component is Player 1's payoff and the second component is Player 2's payoff. (a) Find all the Nash Equibria of this game, in both pure and mixed strategies. (continued) Next, we construct a Bayesian Game by adding the following information structure to the payoff structure above. There are four states in the state space S: 81, 52, S3 and S4. Before she decides what action to take, Player 1 gets one of two signals: u or d.- When the state is s1 or 52, she gets the signal u; when the state is S3 or 5438116 gets the signal 6!.- Before he decides what action to take, Player 2 gets one of two signals: [ or 1'. When the state is 51 or 33, he gets the signal 1: when the state is s; or S4,,he gets the signal 1'. Each player can only observe s/he own signal. We will study the Bayes-Nash Equilibria of this game under different prior probability distributions on the state space S. To specify a BNE, you must specify a pair of strategies for the two players: (Player 1's action if she gets the signal u , Player 1's action if she gets the signal cf; Player 2's action if he gets the signal [, Player 2's action if she gets the signal 1') (b) In your answer to (a), there is a Nash Equilibrium in which neither player uses a pure strategy. There is a prior probability distribution on S for which the BNE has the same (probabilistic) outcome as this mixed- strategy Nash Equilibrium. What is that probability distribution and what is the BNE? Justify your