(Solved):   i would really appreciate if you could help me out. Consider the following \( 3 \times 3 \ ...

 

i would really appreciate if you could help me out.

Consider the following \( 3 \times 3 \) two player normal form game that is being repeated infinite number of times. The discounting factor for player 1 is \( \delta_{1} \) and the discounting factor for player 2 is \( \delta_{2} \). a. Find the total discounted utility for player 2 if player 1 decides to play middle all the time and player 2 decides to play le ftall the time. [5] b. Now suppose both players are following the strategy of part (a) until player 1 decides to play \( u p \) in the 5 th stage. The the new NE after the 5 th stage is (up, right) Find the total discounted utility for player 2 in this case. [5] c. Using the grim trigger strategy, find the minimum value of \( \delta_{2} \). Can you find any anomaly in your calculated value of \( \delta_{2} \) ? [5]