Consider the following 33 two player normal form game that is being repeated infinite number of times. The discounting factor for player 1 is 1 and the discounting factor for player 2 is 2.

leftcenterright

up(15 ,42)(84 ,74)(71 ,27)

middle(53 ,32)(23 ,18)(27 ,85)

down(77 ,75)(74 ,25)(35 ,60)

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 left all the time. [5]

b. Now suppose both players are following the strategy of part (a) until player 1 decides to play up in the 5th stage. The the new NE after the 5th 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 2. Can you find any anomaly in your calculated value of 2? [5]