"As every scientific discipline, game theory also has its own language. The decision makers are called players, even if the decision problem is not a game and the decision makers are not playing at all. The decision alternatives are called the strategies, and the objective functions of the players are called payoffs or payoff functions. Game theory can be divided into two major groups. If there is no negotiation or mediation between the players, and they select social strategies independently from each other, then the game is non-cooperative, otherwise cooperative. The most simple situation occurs if each player knows the set of feasible strategies and payoff functions of all players, in which case we face a game with complete information. Otherwise the game is incomplete. In the case of repeated or dynamic games with perfect information, the players have complete knowledge at each time period about the complete history of the game with all previous strategy selections and payoff values. Games with imperfect information occur if some of the above mentioned information is not available to the players. In most cases, the missing information is considered as a random variable and therefore probabilistic methods are involved in the analysis. If the game is played only ones [sic:once], each player selects a strategy simultaneously with the others and they receive the corresponding payoffs instantly, then the game is static. However in many cases the game is repeated and the set of feasible strategies and payoff values of each time period might depend on the previous strategy selections of the players, in which case we face repeated or dynamic games. The overall strategy of each player consists of his decisions at any time period and in any possible situation of the game at that time period."
Sorry about the length of that. I wanted to be sure I got the whole section because all of it is relevant. Matsumoto and Szidarovsky do not mention role-playing games a single time in their book, so it falls to us to fill in the gap.
Let's start with "payoffs." It must be clearly understood that what's meant here does not include the touchy-feely sentimentality of a game's positive feedback. There are plenty who will argue that this is a "payoff," but we're talking about game theory, where the definition of the word within the context of the subject matter is specific. It's a number. It may represent profit, quantity, any measure that can be used to determine a hard increase describing the player's progression. The payoff is the chief motivation of the player.
Therefore, if we are talking about a GAME (and I presume that's what we're talking about, because we keep calling it a game when we role-play), then no matter what nonsense anyone, ever, tries to feed into the system that experience points, levels, wealth, hit points or any other number in the game doesn't matter, spit in their eye.
A game is about numbers. Anyone who ever tells you different is trying to sell you something.
That is a mighty difficult pill to swallow, particularly since there has been so much propaganda surrounding role-playing games to the contrary that most of the participants have been well and truly snowed. We're told that the game is about 'story' so often that we're inclined to believe it, even when any clear-eyed examination of that statement reveals that it's so vague and insubstantial that we're forced to recognize that it's a jackalope that can't be found.
Yet, saying the game is about "numbers" seems to suck the joy out of things, nyet? Well, trust me, I'm not saying the game is about numbers. It isn't about "story" or "simulation" or "fun" either. Games - all games - are about decisions. It is right there at the lead of the quote. The players are the decision makers who apply strategies to accumulate the numbers or to prevent the loss of the numbers.
I must admit, I find it very hard to define RPGs in the standard terms used to describe games. For example, "cooperative" games are those that emphasize participation, challenge and fun over winning and losing. Usually, a judge is placed in existence who can enforce cooperation among the contestants. This is certainly a description of role-playing.
At the same time, "non-cooperative" games are those in which the players make decisions independently, where any cooperation is self-enforcing. While the DM may prevent player-versus-player, this is not the same thing as making one player help another in a bad situation. Nor does the DM have unilateral power over a player like an umpire has at a baseball game. In many ways, a player and a DM can play "chicken" with one another - a classic non-cooperative game.
Consider "complete" information in a game versus "incomplete." Complete information is that where the knowledge about the other participants and players is available to all, specifically the strengths and objectives. An example of this would be Battleship, where the information is complete but not perfect. We know how many ships the other player has, we know what the other player's objectives are. A more perfect information game would be chess, in which all the pieces are evident and the other player's moves are explicit. This is certainly not a description of role-playing.
On the other hand, games with imperfect information are those where the players are simply unaware of the actions chosen by other players. They will know who the other players are, what their strategies are and the preferences of these other players, but beyond that the information is incomplete. The common example is the prisoner's dilemma, where two players each have two options whose outcome depends crucially on the simultaneous choice made by the other. However, role-playing is not played in the dark like this: in many ways, like chess, the game is played sequentially, so that the players do have knowledge of what other players are doing and are made aware of the DM's intentions when the DM reveals the actual thing about which the players are to make a decision. Moreover, unlike the prisoner's dilemma, the DM has nothing to win and nothing to lose. So this is not a straight-forward description of role-playing, either.
Finally, we have "repeated" games and "simultaneous" games. Repeated games, like Battleship, Chess or even Chicken, are examples where although the play is repeated, the manner in which we play alters according to the past decisions we've made and what we now think about our opponents. If we play chess again and again, we won't just play the same single game, each of us making the same moves; we will try different moves, creating different "games," though the dynamic of the game will remain unchanged - we will have the same objective each time we play. In some ways this describes role-playing, as we will use the same kinds of attacks or the same strategies, both as players and DM; in most ways, however, it does not, as sessions of an RPG cannot be seen as repetitions of the same game.
Repeated games are sequential, in that the players take turns. This is different from the simultaneous game, where both players choose their actions at the same time, without being sure of the other's. An example of this would be rock-paper-scissors.
Again, in many ways role-playing fits the sequential formula. The combat system takes turns, the players wait for the DM to describe the setting and situations and the DM waits for the players to explain their intentions. At the same time, considerable parts of the game are definitely simultaneous; the DM withholds a ton of information from the players, forcing the players to act in the blind, while the players are able to do the same to the DM, not revealing their full intentions or plans until the critical moment. In a lot of ways, role-playing can be like rock-paper-scissors.
It is no wonder with all this lack of clarity that there are endless arguments about what role-playing is, how it fits into game theory, what the objectives are and so on. Because it is so mutable, it can shift from one type of game to another, depending on the player's decisions and the DM's proclivities. A particular campaign can emphasize the sequential element and present nearly perfect information for the participants, whereas another campaign can do the exact opposite, with both campaigns presenting the same game.
Once again, this helps me to understand why I love this game so much. It is clearly superior to the lexicon of games that others have created and is clearly only in its formulative stages in terms of our understanding the game. As I pointed out, the game theory book that I've been quoting does not mention RPGs or role-playing a single time - though it was published this year, in 2016.
Such an opportunity for some would-be doctoral student!