# Probing Outcome-Level Resemblance and Mechanism-Level Alignment in LLM Risk Decisions: Evidence from the St. Petersburg Game

arXiv: https://arxiv.org/abs/2606.04978 · HTML: https://mlsanity.com/paper/2606.04978/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Artificial Intelligence, Values and Alignment](https://mlsanity.com/paper/2001.09768/) (2020)
- [Thinking Fast and Slow in Large Language Models](https://mlsanity.com/paper/2212.05206/) (2022)
- [Cognitive Bias in Decision-Making with LLMs](https://mlsanity.com/paper/2403.00811/) (2024)
- [INVESTORBENCH: A Benchmark for Financial Decision-Making Tasks with LLM-based Agent](https://mlsanity.com/paper/2412.18174/) (2024)
- [StockBench: Can LLM Agents Trade Stocks Profitably In Real-world Markets?](https://mlsanity.com/paper/2510.02209/) (2025)
- [CliMedBench: A Large-Scale Chinese Benchmark for Evaluating Medical Large Language Models in Clinical Scenarios](https://mlsanity.com/paper/2410.03502/) (2024)
- [INS-MMBench: A Comprehensive Benchmark for Evaluating LVLMs' Performance in Insurance](https://mlsanity.com/paper/2406.09105/) (2024)
- [Characterizing Bias: Benchmarking Large Language Models in Simplified versus Traditional Chinese](https://mlsanity.com/paper/2505.22645/) (2025)

## Abstract (arXiv)

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.