Behavioral Mathematics for Game AI

Human behavior is never an exact science, making the design and programming of artificial intelligence that seeks to replicate human behavior difficult. Usually, the answers cannot be found in sterile algorithms that are often the focus of artificial intelligence programming. However, by analyzing why people behave the way we do, we can break down the process into increasingly smaller components. We can model many of those individual components in the language of logic and mathematics and then reassemble them into larger, more involved decision-making processes. Drawing from classical game theory, “Behavioral Mathematics for Game AI” covers both the psychological foundations of human decisions and the mathematical modeling techniques that AI designers and programmers can use to replicate them. With examples from both real life and game situations, you’ll explore topics such as utility, the fallacy of rational behavior, and the inconsistencies and contradictions that human behavior often exhibits. You’ll examine various ways of using statistics, formulas, and algorithms to create believable simulations and to model these dynamic, realistic, and interesting behaviors in video games. Finally, you’ll be introduced to a number of tools you can use in conjunction with standard AI algorithms to make it easier to utilize the mathematical models.

Table of Contents

Part I: Introduction
1 Why Behavioral Mathematics?
2 Observing the World
3 Converting Behaviors to Algorithms

Part II: Decision Theory
4 Defining Decision Theory
5 Game Theory
6 Rational vs. Irrational Behavior
7 The Concept of Utility
8 Marginal Utility
9 Relative Utility

Part III: Mathematical Modeling
10 Mathematical Functions
11 Probability Distributions
12 Response Curves
13 Factor Weighting

Part IV: Behavioral Algorithms
14 Modeling Individual Decisions
15 Changing a Decision
16 Variation in Choice