Three Types of Game Theory and Their (Mis)Uses in Literature

(Here’s my post, finally—please forgive the lateness)

I’ve started to work on the preliminary reading and research for my seminar paper, and I wanted to use this post to talk through two of the articles that I’ve looked at on aesthetic game theory, and whether or not that’s really an appropriate angle.

As I mentioned in another post, part of my idea is to look at tests of love and chastity as games. However, as I’m reading through papers I’m realizing that there are three very distinct “game theories” being discussed, and that it’s important to delineate these in order to make any kind of clear argument. They are roughly, as follows:

1.   Economic/behavioral game theory. This is the type of game theory that pertains to situations in which players may choose to cooperate or to defect, and often have imperfect knowledge of the state of the game. Chance and probability can be involved here (either for Bayesian updating as new information becomes available, or to determine expected utility). The objective of these games is to maximize utility. Utility is determined by the needs and wants of the individual player.
   
2. Combinatorial game theory. This is a branch of discrete mathematics. I hadn’t really expected it to come up but in the article “What Maggie Knew: Game Theory, "The Golden Bowl," and the Possibilities of Aesthetic Knowledge,” Jamesian scholar Jonathan Freedman (purposefully or otherwise) confuses combinatorial and economic game theory and begins comparing the situation in “The Golden Bowl” to a game of tic tac toe. This actually has interesting rhetorical implications, since combinatorial games—especially trivial ones like tic tac toe—often have a predetermined winner based on which player has the first move, assuming that all play is optimal. Combinatorial games are not probability based and generally afford all players complete knowledge of the state of the game. They also lack the moral or ethical component of economic games, which may entail the option to cooperate or to defect. The goal here is to obtain a mathematical victory.
   
3.  Game studies. This is the study of games as literature, most often applied to digital media (video games, interactive fiction, etc.) While game studies may involve examining or producing computer code, it is rarely mathematical. This field looks at the elements of the game, the conditions for winning/loosing, and the constraints of the game among other things. One of the defining concepts here is procedural rhetoric—the idea that the options made available to the players and the moves that they are either allowed or forbidden to make are rhetorically significant.

These are very different theoretical frameworks and, I’m realizing that there is a real danger of letting these things get tangled up in one another because they are similarly named and all pertain—broadly—to games as a medium.

In my paper, I will not be concerning myself with combinatorial games. While the ideas of a mathematically predetermined outcome and optimal play might actually be worth exaining, for what I’m trying to discuss (the unviability of love tests, and the rhetorical moves that must be made in order to make them viable) I don’t believe that this is relevant. If anything, it leads to something of an oversimplification.

I am still in the process of deciding whether or not economic game theory makes sense as a model here, and that’s part of what I’m trying to work out in this post. In some ways, it fits. The husband has the option to test his wife, or not to test her. The wife has the option to be faithful or unfaithful. However, by this model, the love test actually is a viable option. Setting this up as a two player game suggests that there actually is a reasonable utility in performing the test. Constructing a more nuanced model that accounts for the intricacies of the situation would require quantitative measures of utility and the probability of any given situation. Since all the data here is qualitative, any attempt to assign such values strikes me as arbitrary and unmathematical. While a multistep game and updating probability could be used to discuss the ongoing nature of the test and the inability to produce positive evidence of chastity (which is a negative trait, being the absence of extramarital sex), this would also need to be done in broad strokes. There may be a way to model this situation using behavioral/economic game theory, but at the moment I’m not quite grasping it. More so, I haven’t decided whether or not trying to model the possible outcome in a pseudo mathematical form actually adds value to my argument.

As such, it seems that this is not actually a combinatorial or economic game theory but game studies that provides the best model for looking at the love test. This model moves the focus onto the actual procedures of the game in a way that would make it possible to ask questions about the lack of an endpoint and what each side must do to “win.” It also opens up the fact that the set of possible outcomes changes when the game is initiated. It is only by starting the love test that it becomes possible for Lear or Posthumus Leonatus to lose, since neither one actually doubted the faith of the women receiving the test prior to initiating the test.

(TLDR: I’ve been reading the wrong articles.)