I've been given the SPNE through backward induction, I just want to understand how to interpret the equilibria properly.
The SPNE: $(agi,de)$ and $(bgi,df)$
For instance, how would I interpret $(agi,de)$?
Please let me know if the following would be an accurate interpretation of the above:
- If A chooses a first, then B will play d.
- In the event that we end up on the right hand side of the extensive form, B will select e and A will subsequently select g. However, if given the opportunity, A will select i.
This is supposed to be a complete contingent plan of action for both players (i.e. if it were in matrix form then we would be looking at all possible strategies for all players).
I find the first part quite easy, i.e. If A selects a, then B will select d which can be represented by $(a,d)$. However, I am getting confused when I have to account for all possible strategies that could be played $\rightarrow$ $(a \color{blue}{gi},d \color{blue}{e})$. I would appreciate it if you could offer some advice.