The GNS Theory is a model for role-playing games that covers three distinct approaches. Gamism refers to "playing to win", narrativism refers to "telling a story", and simulationism refers to the process of interacting with a consistent world. While the GNS theory itself is considered a bit outdated (the author of the theory now uses the Big Model instead), it still has repercussions when it comes to believability. While it might seem that only simulationism is relevant, both gamism and narrativism reflect different modes of thinking that can also be compared, contrasted, and included in a believable model.
Gamism: Goal Completion
The idea behind gamism is the idea behind "context-free" games or sports: the rules of the game are the rules of the game, and that's it. The goal of the game is to win according to the rules. This is not a problem in a game that has no context or story behind it, but can be problematic when the "rules" don't exactly match up with the "reality". For example, when I analyzed Company of Heroes, I noted that there were many parts of the game that simply don't reflect a World War 2 concept; the technology and reality of the situation is so different that "real" tactics wouldn't work. Hence, someone playing CoH effectively is going to use strategies and tactics that are not at all comparable to real ones.
However, this is not always a bad thing. Gamism only affects believability when the gameplay is itself unrealistic (or at least inconsistent with the presented universe). It's also possible to make games where, for the most part, logical tactics work. The Total War series is a good example of this, because the basics of combat are the same as in reality. The roles of various unit types (spearmen, archers, cavalry) corresponds to reality, and the presence of factors like fatigue and morale allows for tactics that reflect reality more closely than the average RTS. It's not wholly realistic, of course, but it's closer than most games. This means that "real tactics" translate fairly well to Total War.
Really, the objectives of a gamist player and the objectives of a real or in-universe strategist are not particularly different. Each is attempting to get the best results with the resources they have; as I've discussed, strategies that are considered "cheap" in a game would be considered innovative in real life. It's the differences that make it problematic; when the characters and players are relying on different strategies, it cuts down on the possibility for emergent storytelling when "what the characters see" is not "what the player sees". The decisions the player makes would not make sense to the characters, and that is where the issue arises.
If the gameplay elements are explained, then it's acceptable: there's no morale because the units are robotic, weapons function "unrealistically" but consistently, magic works the same way in the narrative that it does in the game, etc. This is because the gameplay is still part of the story, and thus emergent stories can still be generated. The gamist viewpoint is only disruptive to believability if it emphasizes the cracks and flaws in the game system with relation to the setting being depicted; in that way, it can be seen as pointing out errors, rather than being an error itself. If a specific choice doesn't make sense in the universe, it shouldn't be in the rules.
Narrativism: Telling A Story
Narrativism is generally defined as gaming with the intent of telling a story, focusing on things like moral decisions and character developments. It seems to focus more on authorial influence as exerted by the DM, rather than the creation of a natural world. To this end, it focuses on the introduction of themes and morals that the DM's scenarios are meant to evoke or revolve around. To use some examples from The Forge: "Is the life of a friend worth the safety of a community?" or "Does love and marriage override one's loyalty to a political cause?"
Essentially, Narrativism relies on the player's limited perception by making everything outside their perception malleable and random. Even something as simple as a random encounter table or a "fate points"-style reroll mechanic is in some way Narrativist, because it relies on the world changing outside of the player's view. For example, if a player was falling from a cliff and used a fate point, there would be a ledge or branch to catch them. The world changes based on the use or expenditure of meta-concepts. It's a style of gaming that crafts things around the players, rather than putting the players into an already-existing world. In that sense, one can see how it shares concepts with traditional modes of authorship and writing.
While Narrativism has its uses when it comes to ease-of-construction for a DM or game developer, it's not really a "believable" setup in any way. It relies on the world not existing outside what the players can see, which is really one of the most important things about believability: to make a world that feels real, instead of a fictional construct. Obviously there are some times when those kinds of things are necessary, since the DM can't keep track of everything in the world, but the more Narrativism there is, the less plausible the world in general is. It's relying on plot contrivance.
In addition, I personally don't like the concept of Narrativism as "storytelling". The difference between Narrativism and Simulationism comes down to whether the game is treated like a book or like a scenario, and both of those are things that have stories to them. Simulationism is the story of events that are assembled logically, while Narrativism is more based around DM influence. To me, this makes it feel more forced, and hence more fake: while it certainly may be touching to bring up an issue like divided loyalties or priorities, to me it has more impact if it's something that makes sense in the context of the game, rather than simply being delivered with no connection to logical events.
It's almost a cutscene mentality; sure, you had your fun playing the game and doing stuff, but the DM has an agenda to push, and the choices he asks of you are going to reflect that. The idea that character development and so on can only come out of Narrativism ignores the fact that Simulationism is about portraying events, and events are what cause character and plot development, not pre-chosen themes. The idea of a story being chosen ahead of time runs largely counter-intuitive to the kinds of stories that I endorse, specifically the concept of an emergent story.
Simulationism: Creating a Reality
The simplest way to talk about Simulationism is to say it's about being there. It's about being x character in y location with z things to interact with. It's not just the direct setup of Gamism, though, because "being x character in y location" also has roleplay implications and would affect how actions are taken and the game is played. It is centered around being a character and acting as the character would, with all the tools and information available to that character.
Simulationism is the most directly "believable" form of play, in that it is a style that specifically attempts to include the concept of believability. It relies upon making the world deep and complex so that it can be interacted with, whereas Gamism and Narrativism are both concerned with surface elements. In a Simulationist environment, everything needs to exist in case the players choose to interact with it, or in case it affects the players in some other way. Things exist not just because "they can" or because "it makes the world feel more real", but because that's part of the gameplay. Everything can be interacted with, hence everything has to exist.
In essence, the more details there are in a world, and the more fleshed out it is, the more useful it is from a Simulationist perspective. This is because all those details are things that can be used by the player. Even something as simple as timekeeping adds a dimension to the gameplay, and the closer the game is to the intended reality, the more useful it is for getting into the mindset of the character, rather than periodically leaving to adopt the mindset of the game player.
There's not a lot more to say in defense of Simulationism, because it is believability. Believability and all its values are an intrinsic part of the concept. Every other article on this blog applies to the concept of Simulationism. A key point, though, is that Simulationism doesn't have to be totally detail-obsessed; instead, it's just important to realize that every detail added is a new mechanic or concept for the players to work with, and if one really wishes to connect the player and the character, the two must be in a position that their logic leads to the same place.
1) Gamism treats the "universe" as irrelevant, yet its goals are not totally contrary to immersion and believability; as long as the game rules accurately represent the universe, gamism is not incompatible with those things.
2) Narrativism relies upon an authorial perspective, and thus is anathema to believability. It does not treat the world as "real", it treats it as malleable and protagonist-centric.
3) Simulationism is believability, and shares all its values.