In professional real estate negotiations, an offer is only serious (and legally binding) if it is put in writing. Therefore, make all serious offers in writing. By putting the offer on paper you set an anchor point to begin the rest of the negotiation.
But sometimes an offer in writing is used as a fishing expedition, e.g. a low-ball offer just to see how the seller will respond. When that happens, responding in writing could very well be a waste of time. You might even try laughing it off with a comment similar to, “Sure, we would all love to get something for nothing. Check back with me when your buyers are serious.” Or the seller could respond in writing with a slightly lower price to signal, “I am willing to negotiate but I will not give my house away.”
If the written offer seems to be artificially low or high, ask the other side to justify the number. What data are they using to arrive at that price? Invite the other agent to help you with the logic on why your client should accept his/her client’s offer. Informal questions that have a, “how would you persuade my client?” focus are a useful strategy for gaining further insight into the negotiation without having to reveal too much yourself.
If you are challenging the other side on an unfair offer, be ready to provide the market research that you have to support your position.