For example, where one party offers to buy a house at 10% below asking price with a 90 day escrow, instead of rejecting the offer, perhaps the seller's response would be: "Yes, the price is very close to asking price, and if the buyers could close in 30 days, it would be a particularly attractive offer." In response, rather than, "But we can't close that soon", the buyers could say, "Yes, 30 days would be agreeable, but we won't have the financing in place for 45 days since we need to close escrow on our own home". "If the price was 10% lower still, we could probably get a bridge loan sooner." Do you see how we are making progress here?
Another lesson from Improv actors is not to ask questions, because they don't build on the story and lots of questions require the other fellow do all of the work on stage--inventing the setting, roles and action. For example, in the image above, if one guy says, "What's for dinner?", the other has to invent a meal. If his invention includes, "Spaghetti and meat balls", the other side cannot fairly respond with "and what's for dessert?". Instead, it's his turn to say, "Yes, spaghetti is delicious and I can eat it all night with my hands." In negotiation, asking questions can cede power to the other party, at least temporarily, putting both of you in the spotlight unnecessarily and risking giving away too much power and creating a negative interpersonal dynamic. For that reason, you don't want to start a negotiation with, "what do you propose?" but rather by suggesting a proposal which can be refined as the narrative builds.
Finally, improv actors are trained to maintain eye contact. It's essential to send and receive physical cues and to deeply engage with one another. In negotiation, serious listening, without distraction is critical to successful outcomes. You don't want to lose sight of your objectives or your negotiating partner!