Consider the following game for which we define the following notation. og: Player 1's probability of...

 

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Consider the following game for which we define the following notation. og: Player 1's probability of playing r if type g, : Player 1's probability of playing r if type b, ,: Player 2's probability of choosing u after observing a choice of r by Player 1, 1: Player 2's probability of choosing u after observing a choice of / by Player 1, Pr(gr): Player 2's belief that Player 1 is type g if 1 has played r, Pr(g): Player 2's belief that Player 1 is type g if 1 has played 1. (6,4) d (4,2) 1 r G 0.5 N 2 B 0.5 (6,1) d (4,2) (7,4) d (5,1) (5,1) (3,2) Make sure you round your answers to 3 decimal places if necessary. This applies to all parts of this question. (i) (1 mark) If og = % = 1, what are consistent beliefs for Player 2? only one consistent value for Pr(g|r), enter that value into both fields). Pr(g|r) (if there is (ii) (1 mark) If og = = 0, what are consistent beliefs for Player 2? only one consistent value for Pr(g|r), enter that value into both fields). Pr(g|r) (if there is (iii) (2 marks) If og = and = 1, what are consistent beliefs for Player 2? there is only one consistent value for Pr(g|r), enter that value into both fields) < Pr(g|r) (if (iv) (6 marks) There exists at least one PBE in which all player types play pure strategies and in which g = 1. In all these PBE, 01 = (v) (2 marks) and beliefs in these PBE are, Pr(g|r) (if there is only one consistent value for Pr(g|r), enter that value into both fields) Pr(g|!) (if there is only one consistent value for Pr(g|1), enter that value into both fields). Consider the following game for which we define the following notation. og: Player 1's probability of playing r if type g, : Player 1's probability of playing r if type b, ,: Player 2's probability of choosing u after observing a choice of r by Player 1, 1: Player 2's probability of choosing u after observing a choice of / by Player 1, Pr(gr): Player 2's belief that Player 1 is type g if 1 has played r, Pr(g): Player 2's belief that Player 1 is type g if 1 has played 1. (6,4) d (4,2) 1 r G 0.5 N 2 B 0.5 (6,1) d (4,2) (7,4) d (5,1) (5,1) (3,2) Make sure you round your answers to 3 decimal places if necessary. This applies to all parts of this question. (i) (1 mark) If og = % = 1, what are consistent beliefs for Player 2? only one consistent value for Pr(g|r), enter that value into both fields). Pr(g|r) (if there is (ii) (1 mark) If og = = 0, what are consistent beliefs for Player 2? only one consistent value for Pr(g|r), enter that value into both fields). Pr(g|r) (if there is (iii) (2 marks) If og = and = 1, what are consistent beliefs for Player 2? there is only one consistent value for Pr(g|r), enter that value into both fields) < Pr(g|r) (if (iv) (6 marks) There exists at least one PBE in which all player types play pure strategies and in which g = 1. In all these PBE, 01 = (v) (2 marks) and beliefs in these PBE are, Pr(g|r) (if there is only one consistent value for Pr(g|r), enter that value into both fields) Pr(g|!) (if there is only one consistent value for Pr(g|1), enter that value into both fields).