[tabako]

If you use backward induction to know what B is going to play, assume A has this information as well. Just do the same thing that you did to figure out what B will play. A will pick the choice that maximizes his payoff, assuming B plays optimally.

There will be multiple equilibrium if, for example, B is indifferent between two choices. In this case, just assume he picks one or the other, and then use backward induction from there to find out what A would do under either circumstance. These separate cases will make up the different equilibriums.