Entry game sub perfect Nash equilibrium

Question

What is the intuition behind the Sub game perfect Nash equilibrium in this game? I thought it would be $(E,A,A)$ with payoff $(1,2)$ but apparently it is $(E,T,T)$ with payoff $(-2,-1).$ Please explain. Thank you.

Answer 1

Let Coke be Player~1 and Pepsi be Player~2, so that we are clear about whose payoffs we are talking about.

This is a game with perfect information that can be solved by backwards induction. In the top-right node, Coke plays T because $-2 > -3$. In the bottom-right node, Coke plays A because $1>0$. Anticipating this, Pepsi plays A because they prefer getting 2 to getting $-1$. Finally, anticipating this, in the initial node Coke plays E because this leads to a payoff of 1 instead of 0.

The equilibrium is $(ETA,A)$ with payoff $(1,2)$.