Consider the following game tree for some two-player game with incomplete information, and answer the questions...

 

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Consider the following game tree for some two-player game with incomplete information, and answer the questions given below. N H P2 U/1 D Plx 0.5 L P2 0.5 Ply U Ly P2 D H P2 D AD D U U 2,-5 4,0 3,2 5,0 2,2 3,0 0,2 1,0 (a) Draw the matrix that represents the normal form of the game given above. Notice that Nature chooses with equal probability the type of player 1, either X or Y, which only player 1 observes. (b) If player 2 could commit in advance to a certain pure strategy that he would follow regardless of player 1's choice of strategy, expecting that player 1 would then choose his best response, what would be that strategy of player 2? What would be player 1's best response to this strategy? (c) Find all pure strategy Bayesian Nash equilibria of this game. Is the pair of strategies you found in part (b) one of them? Explain why or why not. (d) Find all pure strategy perfect Bayesian equilibria of this game. Is the pair of strategies you found in part (b) one of them? Explain why or why not. Consider the following game tree for some two-player game with incomplete information, and answer the questions given below. N H P2 U/1 D Plx 0.5 L P2 0.5 Ply U Ly P2 D H P2 D AD D U U 2,-5 4,0 3,2 5,0 2,2 3,0 0,2 1,0 (a) Draw the matrix that represents the normal form of the game given above. Notice that Nature chooses with equal probability the type of player 1, either X or Y, which only player 1 observes. (b) If player 2 could commit in advance to a certain pure strategy that he would follow regardless of player 1's choice of strategy, expecting that player 1 would then choose his best response, what would be that strategy of player 2? What would be player 1's best response to this strategy? (c) Find all pure strategy Bayesian Nash equilibria of this game. Is the pair of strategies you found in part (b) one of them? Explain why or why not. (d) Find all pure strategy perfect Bayesian equilibria of this game. Is the pair of strategies you found in part (b) one of them? Explain why or why not.