As part of healthy negotiations it's common for terms to be negotiated, not just the price. It's possible that a lower price is not always in the buyer's best interest.
One of those times can be if the seller is willing to pay a lump sum to the buyer's lender at closing. It's really just prepaid interest, but the effect on a buyer's payment can be substantial. It's called "buying down" the rate because the seller's payment is used to get the buyer a lower ("buy down") mortgage rate, resulting in lower monthly payments.
I'm no mortgage broker, but you might be surprised at the effect a 1/2 percent lower mortgage rate has on monthly payments, AND how little it might cost a seller.
These days it's more common for sellers to pay all or part of a buyer's closing costs, which is certainly valuable to a buyer, but work with both agents and the buyer's lender to examine the possibility of buying down the rate to make a better deal for both buyer and seller.