Many games have opposed skill rolls, for when two characters are trying to achieve opposite effects in competition with one another. There are symmetrical examples, such as a tug-o-war, in which both characters are trying to use their strength (or athletic skill) to pull in different directions. And there are asymmetrical examples, such as when one character is trying to read the other's mind, while the second character is resisting the attempt.
The essential distinction compared to normal skill rolls is that you don't just succeed or fail on your own skill. You have to do better than your opponent. Which also introduces the possibility of doing the same as your opponent and ending up in a stalemate. There are a few ways to handle this.
You can simply declare no winner and both characters have to give up and try something else. Or you can have them deadlocked, neither able to press home an advantage, for some period of time (a game turn or round or whatever), and then have them roll again. This approach raises the possibility that they could be locked in the stalemate for an extended period of time.
If this happens, you can let other characters do stuff around them to try to distract them! (If they're present...)
Commentary by memnarch (who has not seen the movie)
Hm, Han Solo must have done something really personal if this is like the movie. Wanting the map still feels the more likely topic, however, as I can guess at the chain of events there more easily with just the visuals. Finn gets caught as a traitor, the people that broke his cover to Rey notify Kylo and/or the First Order, Kylo comes for the map, finds Rey and tries to get it from her but fails, and then knocks her out to bring her here to continue attempts without the Resistance interrupting. Really, if Snoke's commands are close like I'd assumed (comic names aside), then Han's location is just a big distraction. And even with the bad temperament Kylo has shown, I don't think the producers would make Kylo's villain ball that big to go off on this tangent.
Person stuck to a chair versus person who can walk around and get things like food and water; I think I know who wins in the end there. If Kylo is stupidly insistent on getting this information from Rey, there's a number of things to do to try and weaken her mental fortitude, starting with just trying the same thing every day until Rey fails a save. And while there's probably a number of various villainous tortures that Kylo (famed for liking bad ideas) probably would go with, going the other direction could actually work better. Providing lots of pleasant distractions and getting other people involved that just talk about useless miscellany before springing a sudden question attempt could work very well. I can't think many people could mentally switch topics and instantly put up mental guards if everyone else had just been talking about the latest space soap opera series or how the last crop of space turnips fared for six hours prior.
Commentary by Keybounce (who has not seen the movie)
[Keybounce's comments will appear here when received.]
Kylo Ren: Tell me where your father is.
Rey: As if.
Kylo Ren: You will tell me. Force Suggestion. 9.
Rey: I resist. 10.
GM: Both mediocre rolls. You’re locked in a mental battle.
Kylo Ren: The Force is with you, young Solo. But you are not a Jedi yet.
Kylo Ren: I use Extra Effort. 12.
Rey: I use Extra Effort. 12.
GM: The Force ebbs and flows between you, but neither of you can gain a telling advantage.
Kylo Ren: How long do we keep going like this?
Rey: Potentially forever. Or until one of us dies of old age. I do 300 rounds of walking a day and I don’t eat fried food. How about you?