Extensive form: pareto inefficiency? The question I'm dealing with is:


  Suppose A plays bf, Which of B's strategies would lead to an outcome that is not pareto efficient?


The answer is apparently ei as $(bf,ei)=(0,5)$, but I don't understand why. If this answer is correct, could you please explain why?

My understanding of pareto efficiency is that by moving from $(x,y)$, we cannot make any player better off without making the other worse off. If this is the case, then $(x,y)$ is pareto efficient.

$(x,y)$ would be pareto inefficient if there exists a movement away from $(x,y)$, where a player can be made better off without the other being made worse off.

From $(bf,ei)=(0,5)$, we can move to:

$(4,4), (5,0),(2,2)$

I don't see how we can move to any of these without making B worse off, I think that $(bf,ei)$ represents a pareto efficient outcome.

Any chance you could offer some advice?

Thanks.
Thanks to denesp, I realised that I was only considering outcomes resulting from the following subgame:



If you consider all outcomes within the extensive form, then it is clear that $(2,6)$ pareto dominates $(0,5)$.