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

With the rapid advancement of large language models (LLMs) and their remarkable capabilities in 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 within this decision-making framework adhere to specific probability distributions and require iterative sampling. This arouses our 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: simulation where the exact probability distribution is known, and generation of sequences where the probability distribution is ambiguous. In the first case, the agent is required to give the type and parameters of the probability distribution through the problem description, and then give the sampling sequence. However, our analysis shows that LLM agents perform poorly in this case, but the sampling success rate can be improved through programming tools. Real-world scenarios often entail unknown probability distributions. Thus, in the second case, we ask the agents to change the activity level in online social networks and analyze the frequency of actions. Ultimately, our analysis shows that LLM agents cannot sample probability distributions even using programming tools. Therefore, careful consideration is still required before directly applying LLM agents as agents to simulate human behavior.