Existence of a subgame perfect Nash-equilibrium
Given is the following game
The game is repeated finitely many times and the total payoff is the sum of the payoff from each repetition.
If we assume that $T=2$, is it then possible to find a subgame perfect Nash-equilibrium such that the strategy $(B,L)$ is played in the first stage (first repetition)?
So far as I can count, it shouldn't be possible to construct any threats for $T=2$ such that the $(B,L)$ strategy is played in the first stage. This is due to the Nash-equilibrium laying in $(T,R)$ and it takes at least $T\geq 3$ to ensure that $(B,L)$ is played in the first stage.
Though, I'm not quite sure how to prove my statement. Can any of you confirm/deny my thoughts and help me with some arguments? Thanks.