In the last few years, the estimator proposed by Bajari, Benkard, and Levin ('07) for dynamic games has been gaining popularity. It is relatively straight forward and is one of the only viable options for estimating dynamic games with both continuous state space and continuous decision variables. I have heard from a few people, though, concerns about what it is really identifying (possibly not the structural parameters it's supposed to be identifying).
My question is three-fold. 1) what are the specific concerns about identification with BBL, 2) when do they (not) matter, and 3) is there a way of getting around the identification issues without having to, say, approximate the state/actions as discrete.