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The Social and Economic Behavior of AI Agents Theory and Experiments (Kay-Yut Ch.pdf
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The Social and Economic Behavior of AI Agents Theory and Experiments
1 Introduction . 1
1.1 Overview 1
1.2 Deep Q-Network—A Primer 4
1.2.1 Nonlinear Neural Network Architecture . 5
1.2.2 Q-Learning Formulation 6
1.2.3 Backpropagation and Experience Replay 7
1.2.4 Neural Networks in Practice: A Primer with Keras
and TensorFlow . 8
1.3 The GPT-Language-based Experimental Economics System
(GLEES) . 11
1.3.1 Conceptual Overview of GLEES . 11
1.3.2 A Component-Based Design of LLM Agents 12
1.3.3 Economics Experiment Implementation . 14
1.3.4 Prompt Engineering and Execution Flow in GLEES 16
1.4 Behavioral Economics Frameworks Applied to AI Systems 17
1.4.1 Methodological Framework . 17
1.4.2 Behavioral Dimensions of Economic Choices 18
1.5 Beyond Human Behavioral Frameworks: AI-Specific
Research Challenges . 20
1.5.1 Emergent Behaviors Beyond Objective Functions . 20
1.5.2 Persona Control and Behavioral Variation. 21
1.5.3 Methodological Implications 23
1.5.4 Tacit Knowledge and Ecological Validity in AI
Behavioral Research . 24
References . 26
2 Emergent Social Behaviors in Deep Q-Network-Based Artificial
Agents 29
2.1 Overview 29
2.2 The Trust Game . 30
2.3 DQN Agent Design31
vii
viii Contents
2.3.1 Neural Network Architecture 32
2.3.2 Inputs and Outputs . 32
2.3.3 Agent Objective . 33
2.3.4 Training Protocol 33
2.4 Trust Game Experiments . 34
2.4.1 Emergence of Trust and Trustworthiness 35
2.4.2 Reputation-Based Trigger Strategies 36
2.4.3 Role of Memory in Trust Formation 37
2.4.4 Importance of Stable Partnerships 38
2.4.5 Valuing Future Outcomes Enables Trust . 38
2.4.6 Robustness Across Implementations 39
2.5 Group Bias Experiments . 40
2.5.1 Experimental Design and Agent Modifications . 40
2.5.2 Emergence of In-group Favoritism . 41
2.5.3 Mixed Results of Retraining Mitigation Attempts . 41
2.6 Neural Intervention and Information Flow Analysis42
2.6.1 Neural Ablation Methodology . 43
2.6.2 Elimination of Group Bias Through Neural Ablation 44
2.6.3 Information Preservation Analysis 44
2.6.4 Asymmetric Signal Retention Between Trustors
and Trustees 46
2.6.5 Implications and Limitations 47
2.7 Future of DQN-Agents . 48
2.7.1 Broader Applications of Socially Intelligent Agents . 48
2.7.2 Integration with Large Language Models 48
2.7.3 Neural Mechanisms of Artificial Social Cognition 49
2.7.4 Ethical Considerations for Emergent Social
Behaviors. 49
References . 51
3 Behavioral Analysis of LLM-Based Artificial Agents . 53
3.1 Overview 53
3.2 Risk and Time Preferences 54
3.2.1 Risk Preferences from the GLEES Lottery Task 55
3.2.2 Risk and Time Preferences from Survey-Based
Experiments 56
3.3 Individual Biases in Inventory Decision-Making . 62
3.3.1 Human Behavioral Biases in the Newsvendor
Problem 63
3.3.2 ChatGPT Behavior in the Newsvendor Problem 65
3.3.3 Behavioral Modeling Using Reinforcement
Learning Framework . 68
3.3.4 Summary and Implications71
3.4 Strategic Interaction . 73
3.4.1 First Price Sealed Bid Auction—Private Values 74
Contents ix
3.4.2 Common Value Auction and the Winner’s Curse . 76
3.4.3 Summary and Implications78
3.5 Social Preferences. 79
3.5.1 Overview. 79
3.5.2 Trust and Trustworthiness. 80
3.5.3 Fairness Preferences 82
3.5.4 Summary and Implications83
3.6 Persona Engineering: Techniques, Evidence,
and Measurement. 84
3.6.1 Overview. 84
3.6.2 Persona Engineering Techniques . 86
3.6.3 Empirical Evidence of Persona Engineering . 87
3.6.4 Behavioral Parameter Estimation from AI Choice
Data: An EWA Example 92
3.6.5 Current Limitations and Open Questions 94
3.7 LLM Behavioral Research: Conclusion and Future
Directions 98
3.7.1 Prompt-Driven (LLM) Versus Learning-Based
(DQN) AI Agents 98
3.7.2 Methodological Lessons for AI Behavioral Research 99
3.7.3 Future Research Directions100
References . 101
4 A Mathematical Theory of AI Behaviors103
4.1 Introduction 103
4.2 The Four-Stage Persona Engineering Pipeline . 105
4.3 Text Embeddings: The Mathematics of Meaning . 108
4.3.1 Mathematical Foundations of Text Embeddings 109
4.3.2 Connecting Embeddings to AI Behavior . 111
4.4 Reference-Point Anchored Trait Framework (RATF) . 113
4.4.1 Mathematical Framework: Reference-Point
Anchored Traits . 115
4.4.2 Reference Point Discovery and Cross-Task
Validation: An Empirical Example . 117
4.4.3 Mathematical Framework for Multi-trait Persona . 125
4.5 Conclusion . 129
4.6 Problem Formulation and Objective Function 130
4.6.1 Soft Kendall’s Tau Objective Function 130
4.6.2 Adaptive Smoothing Parameter Selection 131
4.6.3 Objective Function Properties . 132
4.7 Why Spherical Coordinate Descent Was Chosen . 132
4.7.1 Dimensionality Challenge. 132
4.7.2 Gradient Complexity of Soft Kendall’s Tau132
4.7.3 Multi-modal Objective Landscape 133
x Contents
4.7.4 Implementation Pragmatism . 133
4.8 Great Circle Parameterization . 133
4.8.1 Mathematical Formulation134
4.8.2 Geometric Interpretation 134
4.8.3 Degenerate Cases 134
4.9 Two-Phase Optimization Strategy for One-Dimensional
Subproblems . 135
4.9.1 Overview of the Two-Phase Approach 135
4.9.2 Phase 1: Coarse Grid Search . 135
4.9.3 Phase 2: Local Refinement Using R’s
optimize() Function 136
4.9.4 Final Selection 137
4.9.5 Computational Complexity of Two-Phase Strategy 138
4.9.6 Why This Two-Phase Approach Works . 138
4.10 Efficiency Enhancements . 138
4.10.1 Active Set Management . 138
4.10.2 UCB Bandit Selection Strategy 139
4.10.3 Statistical Decay . 139
4.10.4 Computational Complexity Analysis 139
4.11 Convergence and Stopping Criteria140
4.11.1 Improvement-Based Stopping . 140
4.11.2 Validation-Based Early Stopping . 140
4.11.3 Maximum Iteration Limits140
4.11.4 Convergence Diagnostics. 140
4.12 Implementation Details . 141
4.12.1 Hyperparameter Settings 141
4.12.2 Numerical Stability Considerations . 141
4.12.3 Memory Management 142
4.12.4 Error Handling 142
4.13 Algorithm Pseudocode . 142
4.14 Computational Performance Analysis 143
4.14.1 Time Complexity Analysis143
4.14.2 Space Complexity . 144
4.14.3 Convergence Rate Analysis . 144
4.14.4 Comparison with Pure Grid Search . 144
4.14.5 Scalability Considerations. 145
4.15 Sensitivity Analysis and Robustness145
4.15.1 Smoothing Parameter Sensitivity . 145
4.15.2 Grid Resolution Sensitivity145
4.15.3 Local Refinement Parameters 146
4.15.4 Active Set Size Impact 146
4.15.5 Initialization Sensitivity . 146
4.15.6 Robustness to Data Quality147
Contents xi
4.15.7 Cross-Validation Performance . 147
4.16 Conclusion . 147
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