I'm a fan of the Duel of Wits in Burning Wheel. It's a good blend of mechanics and RP, with an interesting rock-paper-scissors meta game.
Hmmm, can you go into detail? Rock paper scissors as a social combat sounds interesting.
Each side starts with a Statement of Purpose - it has to be an affirmative statement, not "I don't
want that to happen." Both sides must agree to the terms before the Duel can start.
Next you determine your Body of Argument (basically Hit Points for the Duel) by rolling your primary argument skill. In the RP, you should try to roleplay the use of that skill (no rolling Intimidate, then roleplaying all your points as a silver-tongued devil).
The Duel itself works like this: each "exchange" (round) has 3 "volleys" (instances in which you may take an action), and you have to "script" (decide what actions to take) an entire exchange at a time. You choose from 7 or so actions - Point, Dismiss, Avoid, Obfuscate, Rebuttal, Feint, and Incite. Point is a basic attack, Dismiss is a powerful attack, but you have to spend the next volley doing nothing afterwards, avoid is a basic defense, obfuscate makes your opponent lose whatever action he had planned, rebuttal is a block+attack, Feint auto-wins vs Rebuttal (and loses to anything else), and Incite makes your opponent lose his next
action. Since you have to script 3 actions at a time, it's very strategic.
The rock-paper-scissors comes from the way the actions interact. Feint beats Rebuttal, Avoid and Rebuttal both mitigate Point and Dismiss, Dismiss beats Obfuscate, and so on.