Evolutionarily stable strategy and Harm thy neighbor

Question

I'm studying ESS, and I have found the harm my neighbor example on wikipedia:

https://en.wikipedia.org/wiki/Evolutionarily_stable_strategy

in Examples of differences between Nash equilibria and ESSes

Now I don't understand why only B,B is ESS. Wikipedia says:

"This dynamic is captured by Maynard Smith's second condition, since E(A, A) = E(B, A), but it is not the case that E(A,B) > E(B,B)"

but we can do the same reasoning with B,B:

E(B, B) = E(B, A), but it is not the case that E(B,A) > E(A,A)

what's wrong?

Answer 1

You failed to swap all the variables. The analogue of $E(A,A)=E(B,A)$ is not $E(B,B)=E(B,A)$ but $E(B,B)=E(A,B)$, and that’s not true; in fact $E(B,B)\gt E(A,B)$, so the first condition for an evolutionarily stable strategy is fulfilled.