Question 3 (24 points) Background Information: There are two players: Player A and Player B. Strategy for Player A: H or L Strategy for Player B: H, M, L If Player A chooses H and Player B chooses H, the playoff for A and B will be 150 and 160, respective;
If Player A chooses H and Player B chooses M, the playoff for A and B will be 140 and 150, respective;
If Player A chooses H and Player B chooses L, the playoff for A and B will be 160 and 110, respective; If Player A chooses L and Player B chooses H, the playoff for A and B will be 120 and 110, respective; If Player A chooses L and Player B chooses M, the playoff for A and B will be 130 and 130, respective. If Player A chooses L and Player B chooses L, the playoff for A and B will be 170 and 150, respective. Questions: If Player A and Player B play the game simultaneously: a) Draw the game for Player A and Player B based on the above information properly. (2 points) b) Find all Nash Equilibrium/Equilibria for the game. (3 points) Now, Player A is the 1st mover, and Player B makes its choice after observing A's choice of strategy: c) Draw the game for Player A and Player B based on the above information properly. (3 points) d) Describe the strategy for Player A and Player B in detail. (4 points) e) Find the strategy profile(s) that constitute all Nash Equilibrium/Equilibria and Subgame Perfect Equilibrium/equilibria for the game. (7 points) f) Player A is still the first-mover, but now Play B CANNOT observe A's choice of strategy when making his/her choice. Find the strategy profile(s) that constitute all Nash Equilibrium/Equilibria and Subgame Perfect Equilibrium/equilibria for the game. (5 points)