The Social and Economic Behavior of AI Agents Theory and Experiments.pdf
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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 Design  31
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 Analysis  42
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 Implications  71
3.4 Strategic Interaction . 73
3.4.1 First Price Sealed Bid Auction—Private Values  74
3.4.2 Common Value Auction and the Winner’s Curse . 76
3.4.3 Summary and Implications  78
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 Implications  83
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 Directions  100
References . 101
4 A Mathematical Theory of AI Behaviors  103
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 Tau  132
4.7.3 Multi-modal Objective Landscape  133
4.7.4 Implementation Pragmatism . 133
4.8 Great Circle Parameterization . 133
4.8.1 Mathematical Formulation  134
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 Criteria  140
4.11.1 Improvement-Based Stopping . 140
4.11.2 Validation-Based Early Stopping . 140
4.11.3 Maximum Iteration Limits  140
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 Analysis  143
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 Robustness  145
4.15.1 Smoothing Parameter Sensitivity . 145
4.15.2 Grid Resolution Sensitivity  145
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 Quality  147
4.15.7 Cross-Validation Performance . 147
4.16 Conclusion . 147
References . 148



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