Yes I agree - it's well known the real estate market functions like a game with both sides bargaining back and forth. There's also psychology involved - each one feeling the other one out. If they didn't like your refusal to accept the 4,0000 hit, they should have said no. If they really want this house, they shouldn't raise it up to 9,000 - they should have dropped it to 3,000 or simply stayed inflexible.

True money doesn't bring happiness but there's principle here. Like I said before you can't let them know you're the least bit anxious - a little like playing poker - you can't let the other guy know what you thinking. If you didn't want to take 4,000 - how will you appear if you accept 9,000? If I were you I would act offended, but quickly state you're fine with 4,000. Keep us posted - I would like to know what you decide.