Solution to Exercise

(T,L)
Neither player can increase its payoff by choosing a different action, so this action profile is a Nash equilibrium.
(T,R)
Player 1 can increase her payoff from 0 to 1 by choosing the action B rather than the action T. Thus this action profile is not a Nash equilibrium.
(B,L)
Firm 1 can increase its payoff from 0 to 2 by choosing the action T rather than the action B. Thus this action profile is not a Nash equilibrium.
(B,R)
Neither firm can increase its payoff by choosing a different action, so this action profile is a Nash equilibrium.

We conclude that the game has two Nash equilibria, (T,L) and (B,R).