The basic categories I see are:
- Numbers/"character skill": comparing skills, rolling dice, spending points
- Tactics: using well-defined mechanics effectively
- Physical player skill: dart guns, boffer, etc.
- Experimentation/deduction: solving puzzles or discovering weaknesses with player logic or trial and error (not skill checks)
- Creativity: coming up with unexpected, not predefined uses for abilities
- Player social skills
Most games have more than one of these, and one potential issue is a noticeable disconnect. One traditional area is when a character's intelligence or common sense don't match the player's. This can lead to the character's stats seeming like informed attributes (the barbarian's as dumb as a rock, but somehow he keeps coming up with clever solutions to all our problems), or leading to awkward GM intervention (the player keeps missing things so the GM regularly interrupts roleplaying to ask for intelligence checks). The same sort of issue often comes up in LARPs, where a character might have better or worse combat stats but, for nerf games and such, player skill at shooting and dodging being as much a factor as character stats in deciding victory, and player skill of choosing when and how to fight being key to achieving desired results with your combat. (Also, player social skills convincing other players that they're on your side can be huge.) To some extent, this can be helped by careful casting, but it can be in tension with other casting goals like avoiding typecasts and giving central roles to new players.
This also comes up against the mechanics vs roleplaying "divide". Should convincing the guard to let you past be based on the GM or NPC's evaluation of your argument (roleplaying-based player skill, potentially evaluated with bias), based on character skill or a die roll (potentially leading to a disconnect between the roleplaying and the result), or based on a combination? (Or you could do something tactical like Burning Wheel social combat.) I think, when it's primarily number-based, it works better to determine success or failure and then roleplay, potentially moving into narration if the player isn't sure how their character pulled it off. Primarily roleplay-based systems can be great, particularly if your game is in a more collaborative-storytelling direction in general, but are very dependent on the group of people (and obviously are hard to handle well in LARPs and other large-group settings).
Allowing player creativity to solve problems can play similarly to roleplay-based diplomacy, where instead of trying to convince a NPC of something the player is trying to convince a GM that something would work. (I'm talking about things like using lye against an acid-spewing monster to create an explosion, or trap making without a trap mechanic.) I've seen this handled well in LARPs, but it helps to have the areas where creativity is encouraged clearly defined and bounds on what's possible clearly pre-determined, to reduce "squeaky-player gets all the things" and "different GMs give different answers" issues.
Taking a step back, it makes sense to think about the priorities for what you're trying to accomplish with your conflict-resolution mechanic. There are a lot of potential goals: authenticity to some in-world reality, some sort of balance or fairness for interesting PvP conflict, making the time taking up by the mechanic not too long or too short, various types of player fun, various types of storytelling agency. Along with this, you want to think about how much you want your game to focus on different types of conflict. A game focused on social dealing might have a contract mechanic to focus on player economics and negotiating skill but have a very simple martial combat mechanic, or none at all. A LARP with balanced martial combat stats focuses more on player skill, though which player skills are most important will depend factors such as whether combats are one-on-one or can involve ganging up, how effective combat is at achieving goals, and what the consequences for losing combat are. In a tabletop, some campaigns focus a lot on the tactics of combat as inherently fun; others mostly assume that the PCs are going to win fights and might be better served by something that takes less time and focuses on things like character development, what sacrifices the PCs are willing to make for victory, or describing cool stunts.
I think that's enough disjointed rambling on conflict systems. Join me next time, when I think about the different things you can try to accomplish with a mechanic more generally.