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

LLMs can appear cautious in risk decision-making tasks, yet cautious-looking outputs do not necessarily indicate alignment with human decision-making mechanisms. We investigate this distinction using the St. Petersburg game as a controlled testbed, a classical paradox in which the expected payoff is infinite, yet humans typically report low, finite willingness to pay. We evaluate 28 LLMs with a structured prompt suite that includes the original game; controlled decision variants that perturb truncation, repeated play, numeric endowment, and occupational identity; a human-perspective prompt that asks models to reason as human decision makers; and paired comparisons between base models and their instruction-tuned counterparts. In the original game, most models generate finite bids, creating the appearance of human-like risk behavior. However, this outcome-level resemblance masks substantial mechanism-level differences. The controlled variants reveal that rather than maintaining human-like behavior seen in the original game, models often shift to conditionally and computationally rational behavior. Human-cue prompting and instruction tuning often lower bids and reduce some visible pathologies, but most mechanism-level response patterns remain largely unchanged. These findings show that behavioral alignment in risk decision-making can be surface-level: LLMs may produce human-like risk decisions without exhibiting human-consistent mechanisms. High-stakes evaluations of LLM decision-making should therefore move beyond outcome similarity and examine whether the alignment is supported by mechanism-level consistency.

The use of large language models either as decision support systems, or in agentic workflows, is rapidly transforming the digital ecosystem. However, the understanding of LLM decision-making under uncertainty remains limited. We study LLM risky choices along two dimensions: (1) prospect representation (based on an explicit representation or outcome history) and (2) decision rationale (explanation). Our study, which involves 20 frontier and open LLMs, is complemented by a matched human subjects experiment, which provides one reference point, while an expected payoff maximizing rational agent model provides another. We find that LLMs cluster into two categories: reasoning models (RMs) and conversational models (CMs). RMs tend towards rational behavior, are insensitive to the order of prospects, gain/loss framing, and explanations, and behave similarly whether prospects are explicit or presented via a history of outcomes. CMs are significantly less rational, slightly more human-like, sensitive to prospect ordering, framing, and explanation, and exhibit a large description-history gap. Paired comparisons of open LLMs suggest that a key factor differentiating RMs and CMs is training for mathematical reasoning.

People make decisions differently in strategic interactions. Some update beliefs like a Bayesian; others exhibit biases like motivated reasoning. Although creators of large language models use simulated humans for safety evaluations and training, they often fail to cover this breadth of human behavior. We argue that cognitive science and economics provide a convenient tool for doing so, making use of mathematical models of human decision-making. We propose an approach that we call Equation-to-Behavior Prompting for guiding large language models to match cognitive models, and evaluate this approach on persuasion games based on legal decision-making. We find that large models can approximate equation-based specifications -- Bayesian updating, affine distortion, motivated updating, and Grether's $α$-$β$ model -- using prompting, but small models fail to do so. However, training small models with reinforcement learning to adhere to mathematical rules, Equation-to-Behavior RL, reduces belief error by 26.5% in out-of-distribution parameterizations. We show that these simulations can help create diverse training environments; training small models to consider different kinds of decision-makers improves average belief change by 2.5%--12% over Bayesian-only training, even when persuading GPT-5-mini. Our work could improve human simulations for training and evaluation in increasingly realistic settings, and could also enable novel research into more complicated mathematical models of human decision-making.