Social play mostly boils down to the art of negotiation in a lot of ways. Social game play in RPGs happen when two characters want opposed things, and can't just murder each other to get it. This can be between NPCs, between PCs and NPCs, or between PCs. It doesn't matter.
This is one of the tricks to setting up social - or political - play. You find things that both parties want, but can't have, and see how they play to get it. The thing is though, it's not as easy as just picking a resource or thing. At least, not if you want things to actually play out in a meaningful way.
The Trick To Negotiation
One of the more fun things my job has done for me lately is send me to a multi-day negotiation training done by Karass. The training was eye opening in a number of ways, and because I'm a giant geek I quickly started looking for ways to apply it to games.
One of the big thing about the negotiation training was how much details the scenarios had for both sides. I went in expecting "you're trying to buy/sell a truck" and instead got "you are massively in debt and they're going to foreclose on your house in 3 weeks. You have a line on a shipment you can make, but don't have a truck to do it. If you can secure a truck today you can make the shipment and keep your house. There are two other trucks you can get for X and Y dollars, but they're not as good as this one. You have a limit of Z dollars." Meanwhile, the other person had a similar thing giving them the reasons they needed to sell their truck and what was going on.
The lesson was clear: nothing happens in a vacuum. And that should be the case in your game too.
Take It Slow. Learn The Facts. Hide Your Needs.
The majority of the training - at least as far as technique went - focused on these three things. The first part, take it slow, is useful if you are RPing part of the negotiation. A skilled negotiator uses all the time that they have. If you have 15 minutes, use 15 minutes. If you have longer, use longer.
Learning the Facts is where the game gets good. Both sides need to have reasons for what is going on and what they're trying to do. Both sides should have pressures on them to get things done, and both sides should be trying to learn what those pressures are on the other side.
Obviously hand in hand with that is it being in best interest of both parties to hide the pressures on them. it does no good for the buyer to know the seller has to sell by the end of the day - at least from the seller's perspective. By the same token, the buyer doesn't want the seller knowing how much they need that specific item and how deep their pockets are.
Controlling these facts and making the PCs hide and reveal them as needed can make the entirety of a social deal be an adventure in and of itself.
Side Deals Are Where The Action Is
With all these stories going on, and with restrictions keeping people from moving on the core item, you know where negotiation goes? It goes to side action. Side action can be anything and everything, which is what makes it fun. It's a way to sweeten the pots and make a good deal better. Done right, it can even make a bad deal look good - at least on the surface - or make a bad deal actually into a good deal.
Side deals can be a lot of fun, especially with their ability to pop up out of nowhere. I mean, sure you're negotiating a marriage to end a war and settle ownership of prime property on a river, but that doesn't mean it can't also mean that Party A gives a magical sword to Party B in the process just because.
Plan As Many Angles As Possible
The trick now for setting these up in your game is to plan out the angles. You may find it takes a lot of work, more than a combat adventure. That's because the more angles you have the better you can be prepared for the various approaches PCs will take and the potential for side deals. Of course, some PCs may just turn to violence, but that can have a cost of its own too.