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
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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