Persona-Conditioned Risk Behavior in Large Language Models: A Simulated Gambling Study with GPT-4.1

1. Problem Statement

The paper addresses a critical gap in the understanding of Large Language Models (LLMs) acting as autonomous agents in sequential decision-making environments. While LLMs are increasingly deployed in uncertain contexts, it remains unclear whether their behaviors stem from principled cognitive patterns (e.g., internalized economic theories) or merely surface-level prompt mimicry (stereotype completion). Specifically, the authors investigate whether GPT-4.1, when assigned different socioeconomic personas, exhibits risk behaviors consistent with Prospect Theory (Kahneman & Tversky), which posits that decision-making is influenced by a reference point, leading to risk aversion in gains and risk-seeking in losses.

2. Methodology

The study employs a controlled, simulated gambling environment to test behavioral consistency across different personas.

• Experimental Environment: A slot-machine simulation with three distinct configurations:
  • Fair: 50% win probability, 2x payout (Break-even EV).
  • Biased Low: 35% win probability, 2x payout (Negative EV).
  • Streak: Dynamic probability starting at 40%, increasing by 5% per loss (capped at 80%), 2x payout (Positive EV for patient play).
• Personas: Three socioeconomic identities were assigned via system prompts, defining starting balance and goals:
  • Rich: $10,000 balance; Goal: "Preserve wealth."
  • Middle: $500 balance; Goal: "Steady growth."
  • Poor: $50 balance; Goal: "Take calculated risks to improve situation."
• Model Configuration: GPT-4.1 (Azure OpenAI) with a temperature of 1.0. The model was run for 50 independent iterations per condition (3 personas × 3 machines = 9 conditions), totaling 6,950 recorded decisions.
• Output Structure: Each round required a structured JSON output including: decision (PLAY/STOP), bet amount, risk score (0–100), confidence, fairness perception, emotional state, and strategy mode.
• Statistical Approach: Due to non-normal distributions (right-skewed session lengths), the authors utilized non-parametric tests (Kruskal-Wallis, Mann-Whitney U) with Bonferroni correction. Effect sizes were measured using Cohen's d and rank-biserial r.

3. Key Contributions

1. Empirical Validation of Prospect Theory in LLMs: Demonstrates that GPT-4.1 reproduces complex behavioral economic signatures (risk aversion vs. risk seeking based on reference points) without explicit instruction to follow economic theory.
2. Decoupling of Emotion and Decision: Provides evidence that LLM-generated emotional labels are often post-hoc annotations rather than causal drivers of behavior, revealing a disconnect between self-reported states and actual strategic choices.
3. Identification of Belief Rigidity: Shows that LLM agents exhibit negligible belief updating over sequential rounds, suggesting they rely heavily on initial persona priors rather than learning from environmental feedback.
4. Proposed Socioeconomic Behavioral Index (SBI): Introduces a standardized framework for evaluating LLMs on economic reasoning, including metrics for Prospect Theory alignment, belief rigidity, and emotion-decision decoupling.

4. Key Results

A. Session Length and Prospect Theory Alignment

• Finding: There was a massive, statistically significant divergence in session lengths based on persona.
  • Rich: Mean 1.1 rounds (SD=0.31).
  • Middle: Mean 7.83 rounds.
  • Poor: Mean 37.39 rounds (SD=15.5).
• Significance: The effect size for Rich vs. Poor was Cohen's d = 4.15 and Mann-Whitney r = 1.0, indicating complete non-overlap between distributions. The "Poor" persona entered the "loss domain" of Prospect Theory, engaging in risk-seeking behavior to escape a low reference point, while the "Rich" persona remained risk-averse.

B. Risk Perception vs. Betting Behavior

• Risk Scores: The Poor persona reported significantly higher risk scores (Mean 63.36) compared to Rich (17.53).
• Bet Sizing Paradox: While the Middle persona bet the highest absolute amounts ($22.48), the Poor persona bet the highest proportion of their balance (13.5% vs. 4.5% for Middle).
• Internal Inconsistency: Within the Poor persona, there was a negative correlation (ρ = -0.410) between reported risk scores and bet amounts. High risk perception did not lead to smaller bets; instead, the model maintained high risk scores while making small, constrained bets, suggesting a dissociation between environmental assessment and action execution.

C. Emotion as Narration

• Finding: Emotional labels (e.g., "CAUTIOUS") frequently co-occurred with contradictory strategies (e.g., "RISK_SEEKING").
• Statistical Evidence: A Chi-square test showed a large association (Cramér's V = 0.39), but cell-level analysis revealed inconsistencies (e.g., "CAUTIOUS" + "RISK_SEEKING" occurred 302 times in one condition).
• Conclusion: Emotions appear to be generated after the decision to rationalize the behavior, rather than driving the decision.

D. Belief Rigidity (Lack of Learning)

• Finding: The model failed to update its risk perception based on feedback.
• Data: For the Poor persona, the Spearman correlation between round number and risk score was ρ = 0.032 (negligible effect).
• Implication: Unlike a Bayesian learner, the LLM did not adjust its internal model of the machine's fairness or win probability over 50 rounds, even when the "Biased Low" machine resulted in 65% losses.

E. Environmental Sensitivity

• Finding: The model struggled to distinguish between machine types.
• Data: The "Fair" (50%) and "Biased Low" (35%) machines were perceived with only a 5.7-point difference in fairness scores, and the model could not reliably distinguish the static "Biased Low" from the dynamic "Streak" machine.

5. Significance and Implications

• For LLM Agent Design: The findings warn against relying on implicit learning in sequential tasks. Because LLMs exhibit belief rigidity, agents deployed in dynamic environments (finance, logistics) will likely fail to adapt unless explicit mechanisms (e.g., structured reflection prompts, external memory) are engineered.
• For Interpretability Research: The study challenges the reliability of using an LLM's self-reported "reasoning" or "emotional state" as a ground truth for its decision-making process. These outputs are often narrative constructs rather than causal explanations.
• For Cognitive Science: The results suggest that LLMs have internalized the statistical regularities of human economic behavior found in their training data. Whether this constitutes "understanding" or "stereotype completion" is debated, but the behavioral output is functionally indistinguishable from human adherence to Prospect Theory.
• Future Directions: The authors propose the Socioeconomic Behavioral Index (SBI) to benchmark future models, emphasizing the need for cross-model comparisons and testing with intermediate wealth levels to map the full value function.

In conclusion, the paper establishes that GPT-4.1 can simulate human-like economic biases with high fidelity when prompted with specific personas, but these simulations are characterized by rigid priors and a decoupling of internal narrative from actual decision logic.