So I just formally accepted a position with a new company (Company A). I haven't begun work with them yet. I informed another company that I was in talks with (Company B) that I had accepted the position. Company B hadn't made an offer yet, but decided to counter-offer once they learned of Company A's offer.
I feel like Company A is the better fit for me at this point, but Company B's compensation is a little bit better. Also, it doesn't seem right to re-open negotiations immediately after I formally accepted an offer. So all in all, I'm pretty committed to Company A.
My question is, should I at least inform Company A of the counter offer? Just to say "Hey, these guys are submitting a slightly better package." Any advice?