Social Interaction can indeed be similar to combat, negotiation of a major political deal comes to mind, but it does not need complex mechanics.

When developing NPCs and other points of social interaction for characters keep in mind two things Personality and Motivations. Take a lot of notes as you play to record details of past interactions that establish these two things.

Motivation is the easiest thing to tackle first.

What does the lord of the realm want? What is he willing to pay for it? Neither of these things need to be money or treasure, he might want peace with the neighboring state and would be willing to trade his daughter in an arranged marriage to ensure peace. Also NPCs might want many things. The lord might want peace, but he might also want a local bandit that is making it difficult to maintain peace captured and is willing to reward those who get him what he wants.

Personality is the second half of the equation. Is the local lord aggressive, passive, miserly or generous? The words used to describe his personality can give methods the local lord will use to achieve his goals.

Lets take for example a rogues operating in the city. Assume the rogues motivation is pure and simple increase to his base wealth. His personality will lead to behaviors. An aggressive and uncreative rogue may be more of a thug who robs his victims at knifepoint. An agile and creative rogue might operate as a second story man breaking and entering through upper floors.

The same is true for social negotiations. The lord who wants peace with his neighbor and is willing to trade off his daughter might also be miserly and offer up a poor low value dowry along with that daughter. The gem merchant approached to fence gems acquired in the last adventure might only offer %30 of the value of the gems because he is greedy and wants to rip people off. The local farmer might only desire to have what he needs to harvest his next crop and feed his family.

Once you have some personality and motivations detail to work with then use the Diplomacy skill. For instance, I have a gem merchant in a setting who starts his negotiations for gem value at 50%. Then I use a diplomacy contest (opposed rolls between the players and the merchant) to evaluate swing. For each point the players roll higher than the gem merchant they gain a percent, for each point he rolls higher than the players he lowers his offer.

Good role playing and banter with the merchant, or sweetening the deal with other alternative offers that are creative can sway this further giving the players bonuses to their rolls. Maybe the merchant wants a very specific gem and would be willing to trade acquisition of the specific stone for a permanent increase of the base starting point.

After this I record history of interactions. Every time the players interact with an individual a point is earned with that specific individual. The players can collect these points and cash them in at some point in the future for a really good bonus. Thus the players could build up a relationship with the gem merchant, bring him quality goods which he makes a lot of money on and then at some point the players get a good haul and they cash in their favor. Once they cash it in the counter resets. Also treating the NPC poorly can cause it to reset with no benefit.