The Allure and Limitations of Mathematical Modeling: Game Theory and Trench Warfare

Abstract

We conclude the first part of this book with a critical overview of an application of mathematical theory to a problem in history – a game-theoretic model that was developed more than twenty years ago to describe some surprising behavior in the trenches in the First World War. As we shall see, the model is appealing because it seems to bring some sense to a scary and confusing subject. However, ultimately, I find this particular analysis unconvincing, and I'll talk about why such a model, if wrong, was so persuasive. This is an important step in social science analysis, inside or outside the academic setting: If you're going to claim that you're right and other people are wrong, you'd better also explain why those other people (who were generally not fools) got it wrong. Scholarly journals are littered with proudly “counterintuitive” findings that are counterintuitive for the simple reason that they are wrong and most people's intuition is right. THE PRISONER'S DILEMMA: A GAME-THEORETIC MODEL APPLIED TO SOCIAL INTERACTIONS Mathematical theory can be a powerful tool for understanding social phenomena but can also mislead, as I'll illustrate with an example from my undergraduate thesis, which was in political science. At the beginning of my senior year in college, I reviewed a list of potential advisors and found one who worked on game theory – I was a physics and mathematics major, minoring in political science, and game theory seemed like a good topic.