Well, my repsonse is to immediately lower the offer, not a lot, but enough to test them out. If they do indeed have a lot of interest and I am "under the market" then fine, it means that isn't the place for me.
If the EA is playing games and there isn't loads of interest, he risks seeing a potential bidder moving out backwards.
So I would go the other way to Mr Mans suggestion.
Thats good advise and something I will probably use.