Okay none of us seem to have any hard evidence or know for sure, but I am pretty sure Obama is President now. I am pretty sure it is mostly him directing what Biden is allowed to say, what Biden is required to say, what Biden is required to sign or veto of legislation, what he is required to issue as executive orders. What's in it for him (Obama) I'm not sure but it might be interesting to follow the money there. Won't happen of course. But it might be interesting.
Again not conclusive evidence, but the fact that Obama is not on record as saying Biden should step down strongly suggests he is content to have Biden in the White House.