The buyer is testing you just as you are testing them by countering. The fact is this, what matters is where you end up, not where you begin. Now I do advice my buyers that the way a process starts certainly sets a tone, and so I am not a great fan of low balling. But I advice my sellers to respond to any and all offers that are real - so if this offer is in writing with verification of funds in hand or promised, then I suggest that you do respond by coming off your number a bit, that will put the ball back in the buyer's court and allow you to see what he'll do next.
Good luck. I just worked through several low ball offers and we responded to all of them. In fact we couldn't get them up to an acceptable point, but along the way, several offers came in that were reasonable and we negotiated one of them to an acceptable level and will soon close. That it the other truism in real estate, very often when one offer comes, others follow - like bugs attracted to light. So my recommendation is to work what you have and hopefully you will be able to get this guy in a more acceptable range or others will follow.
Good luck to you,
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