I'm a new GM in D&D 4e. I've quickly found that I perform very poorly when I'm portraying a negotiation between the PCs and one or more NPCs. Even when they have common ground and could easily find something to agree on that would benefit both sides, the negotiations end up with no agreement reached and both parties annoyed at each other. (Of course, when they're "negotiating" with the BBEG, this is the desired result, so this is really only about friendly or potentially friendly NPCs.)
After a recent negotiation failed, I talked to the players out-of-character and said "This is where I wanted to be going with this" and they very graciously hopped back on the railroad, so it's not at risk of derailing the adventure, but how can I learn to portray the negotiation in a realistic and meaningful manner that's compatible with how I want to move the story forward?
To expand: the recent negotiation was between the town sage, who wanted to know everything about the PCs (the meta-reason for this is I wanted them to develop their backstories further, so I can tailor the adventure to them). The PCs wanted the sage to examine an artifact they found and give them some history of the area, hoping they can get him to reveal location that might be the BBEG's headquarters. The result was the PCs got suspicious of the sage interrogating them, and resented his air of superiority, and utterly refused to divulge any details. At that point I explained what I was trying to do; two of the PCs consented to stick around and answer questions.
Best Answer
I've been on the receiving end of a bunch of bad negotiations in RPGs. Real life negotiation training helps, but there's also some RPG specific aspects to keep in mind.
Often, the problem is that there's some adventure hook that requires the PCs to do something that's totally stupid. "Hi, you're level 10, would you like to go on a fetch quest for 100 gp?" Or the classic module Against the Giants, where the locals decide your high level party is guilty of unspecified crimes (vagrancy?) and must go kill 100 giants to atone. Even LG parties respond to that with "You're going to look mighty funny with that longsword sticking out of your ass." Your non-derogatory use of the term "railroad" (generally considered bad) leads me to believe this may be the case - if you expect the PCs to "take the adventure hook" you present them regardless of its desirability and they are trying to live in character and not go for some awful deal their characters at their current wealth and power level would never contemplate, you'll be disappointed.
Now assuming there's at least the makings of a deal, meaning each side has something the other person reasonably wants and might indeed exchange (goods, services, money, etc.) you need to remember that people want to make deals and that they can be win-win.
Allow me to use the framework presented in Getting to Yes, a book on negotiation everyone should read.
Separate the people from the problem. Put yourself in the PCs' shoes. Listen more than you talk. Get them involved. Help them save face at giving in on things. They should ideally be doing the same to the NPC.
Focus on interests behind positions. Ask "Why" and "Why not?" Be hard on the problem, soft on the people. How can everyone's goals be achieved? Don't attack the other person's position, look behind it. When they attack your ideas, ask for advice. Ask questions and pause. "How can we make this deal happen?"
Invent options for mutual gain. Generate a range of options, Use imaginative procedures. What other things does someone have that they'd be willing to do or give away that the other person might value more? It doesn't have to be a flea market "Five dollars! One! Four! Two! Three! Deal!". That's a one-dimensional negotiation. Timing, loot, favors, future goods are all possible. "What else can I throw in?"
Use independent standards. What is this really worth? If someone's being unreasonable, you can show what the item or job is "worth" to others. "These guys will do it for half the rate, but I want you to have the first crack at the loot..."
Develop a best alternative to a negotiated agreement. If one side has to have the deal or they're completely screwed, they are in a bad position. As a result most people have a plan B. As a DM, you need one too, besides "tell them out of character to take the bait." Maybe it's some kind of setup or extortion (e.g. the PCs' rooms get ransacked and a convenient clue is left behind pointing at the people the adventure hook is trying to sic them on. Of course the other negotiating party did it, but PCs are usually dumb and easily pointed in a direction.)
Of course, you can just let events transpire. In your example, the PCs got suspicious of the sage. So? Can they not get the information any other way? Are there no other people they can go to? Do they not plan to just stage a home invasion and interrogate him (normal PC response to something like this)? Your problem is less about negotiation and more about poor adventure design and railroading. Should there really only be one way to proceed in the plot? It's best if not; but if it is then the PCs will eventually have to give in or beat it out of him... I find you always get the best results from handling things in game, not with metagaming and railroading. It may seem expedient now but it's a long term poison for your game.