# 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.

• If A would play $(af)$ while B maintained $(ei)$ the outcome would be (2,6), which Pareto dominates (0,5). Apr 21 '15 at 22:03
• Ah, thank you. I was only considering the outcomes from the subgame initiated after B plays e. If you want to rewrite your comment as an answer, I'd be happy to accept it. Apr 21 '15 at 22:19
• Thank you, but I am content with your answer. Apr 22 '15 at 5:26

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