Behavioral mathematics for game AI

Contents......Page 12
Part I: Introduction......Page 20
1 Why Behavioral Mathematics?......Page 22
Games and Choices......Page 23
Going Beyond Looks......Page 29
2 Observing the World......Page 34
Identifying Factors......Page 35
Finding Hidden Factors......Page 41
Quantifying Observations......Page 43
Needing More Than Observations......Page 47
3 Converting Behaviors to Algorithms......Page 48
Using Numbers to Select......Page 49
Using Numbers to Define......Page 52
Using Algorithms to Construct Numbers......Page 56
Part II: Decision Theory......Page 62
Normative Decision Theory......Page 64
Descriptive Decision Theory......Page 67
The Best of Both Worlds......Page 70
5 Game Theory......Page 74
Starting Simple......Page 75
Asymmetric Games......Page 88
6 Rational vs. Irrational Behavior......Page 98
Perfect Rationality......Page 99
Bounded Rationality......Page 115
Rational Ignorance......Page 124
Combining It All......Page 128
7 The Concept of Utility......Page 130
Decisions under Risk......Page 131
Utility of Money......Page 140
Utility of Time......Page 159
Our Utility of Utility......Page 184
8 Marginal Utility......Page 186
Value vs. Utility vs. Marginal Utility......Page 187
Changes in Marginal Utility......Page 188
Marginal Risk vs. Marginal Reward......Page 200
Defining Thresholds......Page 206
Multiple Utility Thresholds......Page 207
The Utility of Marginal Utility......Page 213
9 Relative Utility......Page 214
Hedonic Calculus......Page 215
Multi-Attribute Utility Theory......Page 217
Inconsistencies......Page 224
Apparent Contradictions......Page 229
The Relative Benefit of Relative Utilities......Page 244
Part III: Mathematical Modeling......Page 246
Simple Linear Functions......Page 248
Quadratic Functions......Page 250
Sigmoid Functions......Page 255
Ad Hoc Functions......Page 259
11 Probability Distributions......Page 260
Identifying Population Features......Page 261
Uniform Distributions......Page 267
Normal (Gaussian) Distributions......Page 269
Triangular Distributions......Page 288
Uneven Distributions......Page 291
Parabolic Distributions......Page 293
Poisson Distributions......Page 295
Distributing the Distributions......Page 298
12 Response Curves......Page 304
Constructing Response Curves......Page 305
Converting Functions to Response Curves......Page 315
Converting Distributions to Response Curves......Page 322
Search Optimization......Page 333
Hand-Crafted Response Curves......Page 335
Dynamic Response Curves......Page 336
Scaling Considerations......Page 338
Weighting a Single Criterion......Page 348
Combining Multiple Criteria......Page 350
Layered Weighting Models......Page 360
Everything Is Relative......Page 367
Part IV: Behavioral Algorithms......Page 368
Defining Decision......Page 370
Deciding What to Decide......Page 372
Analyzing a Single Option......Page 374
Comparing Options......Page 404
Selecting an Option......Page 405
Testing the Algorithm......Page 406
Summarizing the Decision Process......Page 411
15 Changing a Decision......Page 414
Monitoring a Decision......Page 415
Perseverance and Decision Momentum......Page 424
Our Final Decision on Changing Decisions......Page 434
16 Variation in Choice......Page 436
Reasons for Variation......Page 437
Embracing Randomness......Page 441
Selecting from Multiple Choices......Page 443
Scores and Weights......Page 463
Epilogue......Page 466
B......Page 470
D......Page 471
G......Page 472
M......Page 473
O......Page 474
P......Page 475
S......Page 476
U......Page 477
W–Z......Page 478