When you meet conflict resolution, do you mean between the players, or between characters within the IC?

IC wise, I generally trust my players to know what's reasonable and right for what their characters should do. When players first join my rp I emphasise how players should and must be prepared for their characters to be injured or lose - afterall, characters that can always win aren't particularly interesting. Characters who lose, and then rise up to overcome their opponents are simply more interesting. I first established this within the first mission where their enemy was simply that powerful that defeating them wasn't an plausible option, and that retreating was the safer, sane option. Not everything needs to result in a victory. Fortunately, all of my players understand this and not only accept it, but support it. They're all quite ready and willing to have their characters injured or lose because it helps make the story more dramatic and interesting. It's something which has to really come down to trust. I dislike stats and dice systems, they're not my thing at all, afterall I prefer the flexibility of having my characters lose in the way I want without having to have that be decided by a dice roll or stat. 

Now, what happens if a player doesn't understand this? Then it becomes a GM call, and something they should communicate over the OOC. If a player is writing a character to be too powerful then what they should, the GM should inform them, explain what is wrong, suggest ways to improve and ask the player to edit their post. If the player disagrees or continues to suffer the same problem where they don't understand the 'power level' within the rp, then the GM needs to deliberate on whether or not the player is suited for the rp.

Player conflict is the same thing really if it continues and escalates - final say is with the GM, but then again I think your topic means character conflict?