Question 1 (15 points): Consider the following game in extensive form, b t 2 C d Z 1 29 V e 26 X 2 X' 25 w (a) Is this a game of perfect recall? Please describe your answer. (b) Determine the normal form of this game (c) Is there a behavioral strategy of the second player that is equivalent to the following mixed strategy? 8 : [0.2 : (c, g); 02 : (c, h); 0.3; (d, g); 0.3 : (d, h)]. If there is such strategy construct it. If not, then explain why not.Question 2 (10 points): Firms Row Inc. and Column Inc. are answering a request for proposal from a buyer. They can try to sell their products with a passive ptch, agressive pitch, and mildly aggresive pitch. However, their profits depend on what the profits of the other firm are, becuase their products are somewhat complementary of each other. The bi-matrix of profits is as follows: Pc Mc Ac ( 1, 1 2, 4 4,2 Mr |4, 2 1, 1 2,4 Ar \\2, 4 4, 2 1, 1 So the firms could benefit from cooperation but they do not trust each other. So they find trusted intermidiary, whom the firms instruct to find the strategy that maximizes the combined profit of the firms. 12 points Give the LP that this intermidiary will have to solve in order to find recommended strategy? 3 points What would be his strategy? Hint: Recall what correclated equilibrium is and what an NE strategy in correlated equilibrium is.Question 4 (5 points): Consider the following game in extensive form, XI L R 01 02 T B t b 1, 0 x2 X3 1,1 r P -2, 1 3, -1 2,-3 -3.2 (a) Construct a normal form for this game. (b) (Bonus) List all pure equilibria of this game. Which ones of these are subgame perfect