Consider the following game that is played T times. First, players move simultaneously and independently. Then each player is informed about the actions taken by the other player in the first play and, given this, they play it again, and so on. The payoff for the whole game is the sum of the payoffs a player obtains in the T plays of the game.
a b c
A 3,2 5,2 1,1
B 2,6 4,4 1,3
C 1,2 0,2 2,3
(a) How many subgames are there if T = 3?
(b) What is the smallest value of T for which it possible for B and b to be played in the first play of the game, in a subgame perfect equilibrium, even though (B, b) is not a Nash equilibrium in the payoff table above. (For example, is it possible for T = 2, T = 3, T = 4, T = 5?)