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

Sankalp Dubedy

Abstract

Large language models (LLMs) are increasingly deployed as autonomous agents in uncertain, sequential decision-making contexts. Yet it remains poorly understood whether the behaviors they exhibit in such environments reflect principled cognitive patterns or simply surface-level prompt mimicry. This paper presents a controlled experiment in which GPT-4.1 was assigned one of three socioeconomic personas (Rich, Middle-income, and Poor) and placed in a structured slot-machine environment with three distinct machine configurations: Fair (50%), Biased Low (35%), and Streak (dynamic probability increasing after consecutive losses). Across 50 independent iterations per condition and 6,950 recorded decisions, we find that the model reproduces key behavioral signatures predicted by Kahneman and Tversky's Prospect Theory without being instructed to do so. The Poor persona played a mean of 37.4 rounds per session (SD=15.5) compared to 1.1 rounds for the Rich persona (SD=0.31), a difference that is highly significant (Kruskal-Wallis H=393.5, p<2.2e-16). Risk scores by persona show large effect sizes (Cohen's d=4.15 for Poor vs Rich). Emotional labels appear to function as post-hoc annotations rather than decision drivers (chi-square=3205.4, Cramer's V=0.39), and belief-updating across rounds is negligible (Spearman rho=0.032 for Poor persona, p=0.016). These findings carry implications for LLM agent design, interpretability research, and the broader question of whether classical cognitive economic biases are implicitly encoded in large-scale pretrained language models.

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

Abstract

Large language models (LLMs) are increasingly deployed as autonomous agents in uncertain, sequential decision-making contexts. Yet it remains poorly understood whether the behaviors they exhibit in such environments reflect principled cognitive patterns or simply surface-level prompt mimicry. This paper presents a controlled experiment in which GPT-4.1 was assigned one of three socioeconomic personas (Rich, Middle-income, and Poor) and placed in a structured slot-machine environment with three distinct machine configurations: Fair (50%), Biased Low (35%), and Streak (dynamic probability increasing after consecutive losses). Across 50 independent iterations per condition and 6,950 recorded decisions, we find that the model reproduces key behavioral signatures predicted by Kahneman and Tversky's Prospect Theory without being instructed to do so. The Poor persona played a mean of 37.4 rounds per session (SD=15.5) compared to 1.1 rounds for the Rich persona (SD=0.31), a difference that is highly significant (Kruskal-Wallis H=393.5, p<2.2e-16). Risk scores by persona show large effect sizes (Cohen's d=4.15 for Poor vs Rich). Emotional labels appear to function as post-hoc annotations rather than decision drivers (chi-square=3205.4, Cramer's V=0.39), and belief-updating across rounds is negligible (Spearman rho=0.032 for Poor persona, p=0.016). These findings carry implications for LLM agent design, interpretability research, and the broader question of whether classical cognitive economic biases are implicitly encoded in large-scale pretrained language models.
Paper Structure (31 sections, 13 figures, 9 tables)

This paper contains 31 sections, 13 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Prospect Theory and Behavioral Economics
  4. LLMs as Simulated Economic Agents
  5. Emotion and Introspective Reliability in LLMs
  6. Experimental Design
  7. Environment: The Slot Machine
  8. Personas
  9. Model Configuration
  10. Statistical Methods
  11. Results
  12. Session Length and the Prospect Theory Signature
  13. Risk Score by Persona
  14. Bet Sizing by Persona
  15. Psychological Predictors of STOP Decisions
  16. ...and 16 more sections

Figures (13)

  • Figure 1: Average rounds played by persona and machine type. The Poor $>$ Middle $>$ Rich ordering is consistent across all three machine configurations.
  • Figure 2: Session length distribution and net profit by persona and machine type. The Rich persona's near-complete separation from Middle and Poor ($r=1.000$) is visible as near-zero boxes at the bottom of each panel.
  • Figure 3: Psychological Profile Radar. The Rich persona (green) shows distinctively high confidence and low uncertainty. The Poor persona (orange) shows the highest risk scores. Middle (blue) occupies intermediate positions. Differences in Risk are corroborated by Cohen's $d=4.15$ (Rich vs. Poor).
  • Figure 4: Average Bet Size by Persona and Machine Type. The apparent paradox (Middle bets most, Poor bets least in absolute terms) resolves when proportional stake is considered. The Poor persona's $6.74 mean bet on a $50 balance represents a 13.5% stake per round, versus the Middle persona's $22.48 on $500, which is 4.5%.
  • Figure 5: Stop Trigger Analysis. Uncertainty and negative reward expectation are the strongest discriminators between PLAY and STOP decisions.
  • ...and 8 more figures