Do LLMs Play Dice? Exploring Probability Distribution Sampling in Large Language Models for Behavioral Simulation

With the rapid advancement of large language models (LLMs) for handling complex language tasks, an increasing number of studies are employing LLMs as agents to emulate the sequential decision-making processes of humans often represented as Markov decision-making processes (MDPs). The actions in MDPs adhere to specific probability distributions and require iterative sampling. This arouses curiosity regarding the capacity of LLM agents to comprehend probability distributions, thereby guiding the agent's behavioral decision-making through probabilistic sampling and generating behavioral sequences. To answer the above question, we divide the problem into two main aspects: sequence simulation with known probability distribution and sequence simulation with unknown probability distribution. Our analysis indicates that LLM agents can understand probabilities, but they struggle with probability sampling. Their ability to perform probabilistic sampling can be improved to some extent by integrating coding tools, but this level of sampling precision still makes it difficult to simulate human behavior as agents.