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Behavioral Mathematics for Game AI

Book Description

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

  1. Copyright
  2. A Little History and a Lot of Dedication
  3. About the Author
  4. Author’s Preface
  5. In the Game Listings
  6. Introduction
    1. Why Behavioral Mathematics?
      1. Games and Choices
      2. Going Beyond Looks
    2. Observing the World
      1. Identifying Factors
      2. Finding Hidden Factors
      3. Quantifying Observations
      4. Needing More Than Observations
    3. Converting Behaviors to Algorithms
      1. Using Numbers to Select
      2. Using Numbers to Define
      3. Using Algorithms to Construct Numbers
  7. Decision Theory
    1. Defining Decision Theory
      1. Normative Decision Theory
      2. Descriptive Decision Theory
      3. The Best of Both Worlds
    2. Game Theory
      1. Starting Simple
      2. Asymmetric Games
    3. Rational vs. Irrational Behavior
      1. Perfect Rationality
      2. Bounded Rationality
      3. Rational Ignorance
      4. Combining It All
    4. The Concept of Utility
      1. Decisions under Risk
      2. Utility of Money
      3. Utility of Time
      4. Our Utility of Utility
    5. Marginal Utility
      1. Value vs. Utility vs. Marginal Utility
      2. Changes in Marginal Utility
      3. Marginal Risk vs. Marginal Reward
      4. Defining Thresholds
      5. Multiple Utility Thresholds
      6. The Utility of Marginal Utility
    6. Relative Utility
      1. Hedonic Calculus
      2. Multi-Attribute Utility Theory
      3. Inconsistencies
      4. Apparent Contradictions
      5. The Relative Benefit of Relative Utilities
  8. Mathematical Modeling
    1. Mathematical Functions
      1. Simple Linear Functions
      2. Quadratic Functions
      3. Sigmoid Functions
      4. Ad Hoc Functions
    2. Probability Distributions
      1. Identifying Population Features
      2. Uniform Distributions
      3. Normal (Gaussian) Distributions
      4. Triangular Distributions
      5. Uneven Distributions
      6. Parabolic Distributions
      7. Poisson Distributions
      8. Distributing the Distributions
    3. Response Curves
      1. Constructing Response Curves
      2. Converting Functions to Response Curves
      3. Converting Distributions to Response Curves
      4. Search Optimization
      5. Hand-Crafted Response Curves
      6. Dynamic Response Curves
    4. Factor Weighting
      1. Scaling Considerations
      2. Weighting a Single Criterion
      3. Combining Multiple Criteria
      4. Layered Weighting Models
      5. Everything Is Relative
  9. Behavioral Algorithms
    1. Modeling Individual Decisions
      1. Defining Decision
      2. Deciding What to Decide
      3. Analyzing a Single Option
      4. Comparing Options
      5. Selecting an Option
      6. Testing the Algorithm
      7. Summarizing the Decision Process
    2. Changing a Decision
      1. Monitoring a Decision
      2. Perseverance and Decision Momentum
      3. Our Final Decision on Changing Decisions
    3. Variation in Choice
      1. Reasons for Variation
      2. Embracing Randomness
      3. Selecting from Multiple Choices
      4. Scores and Weights
  10. Epilogue
  11. Index