# Why Game Theory?

One of my main research interests is *Game Theoretic Pragmatics*. Pragmatics is, to put it simply, the way people choose to use language -- how context, inference, prior knowledge, and other factors that are not purely *structural* affect meaning and communication.

So what does that have to do with Game Theory?

The answer is: a surprising amount. First, it's important to know what I mean by Game Theory.

Older readers will be surprised to learn that many people under 30 naturally assume Game Theory refers to...the theory behind creating video games. This is incorrect. On the other hand, most people who remember the Cold War have very strong feelings about Game Theory -- with ominous thoughts about military strategy, Mutually Assured Destruction, and nuclear nightmares -- but also don't quite see how that could be applicable to the study of language.

Game Theory is the branch of mathematics that deals with strategic decision making by thinking agents. It originated with the mathematicians John Von Neumann and Oskar Morgenstern and their book *Theory of Games and Economic Behavior*, published in 1944. For most people, the best known figure in Game Theory is the Nobel Prize winner John Nash (played by Russel Crowe in the biopic *A Beautiful Mind*), whose dissertation was, famously, a mere 28 pages long. While the study of rational (and irrational) decision-making is useful in military strategy, it need not be limited to macabre studies on nuclear annihilation, and it is in fact applicable to a wide range of non-military areas of research, including evolutionary biology and urban design.

My interest in Game Theory is twofold. I am interested in:

- Modeling the ways in which speakers make choices when interacting, taking into account their beliefs about their interlocutors. In this respect, I model speech acts as plays in an extended game. I'm especially interested in how people choose to imply and infer meanings. The class of games known as
*Signaling Games*are particularly useful here. - Modeling language change using the mathematics of
*Evolutionary Game Theory (EGT).*EGT originated with John Manyard Smith and George Price. Their seminal 1973 paper applied Game Theoretic models to animal conflict. EGT is primarily concerned with strategies in competition. In evolutionary biology, this means using replicator dynamics to model gene flow (among other things). In linguistics, this means modeling linguistic behavior (pronunciation, word choice, etc.) as strategies in competition.

So what does this mean practically, in terms of actual projects?

Well, I'm currently working on a few projects using Game Theory:

- I'm just finishing a paper on
*Microaggression*, in which I argue that -- unfortunately and contrary to popular belief -- it is a property of coversational implicature that a hearer cannot be 100% certain what is meant by a verbal microaggression. I do so by modeling microaggression as a Bayesian Signaling Game: players form beliefs over the possible types of other players. Then, when one player sends a signal, the receiver can update their prior beliefs about that player's type before choosing an action. - I am using Distributed Morphology (DM) and EGT to model verbal suppletion as the result of small-scale statistical decision-making about politeness and coordinating behavior iterated over a large number of verbal decisions, over generations. Basically, I'm arguing for each independent form in a 'paradigm' as a strategy in a verbal ecology, and using replicator dynamics to model change. I am then comparing those predictions to the historical record, using various corpora.
- I am using similar methods to model the 'euphemism treadmill' as predation. I compare predator-prey dynamics modeled in a Lotka-Volterra distribution to the patterns of emergence, adoption, and replacement of euphemisms, using various corpora.

If the above was Greek to you, don't worry! There will be future posts about each, in layman's terms.

Ultimately, Game Theory is just one of many possible tools in approaching language variation and change. Given an approach to linguistics, especially pragmatics, which treats language acts as decisions made by thinking agents (this is emphatically *not* a given for many linguists!), Game Theory provides an enormous number of incredibly useful tools for thinking about language, modeling change, and making and testing predictions about language use.

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©Taylor Jones 2014

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