Beyond Nash Equilibrium: Bounded Rationality of LLMs and humans in Strategic Decision-making

Large language models are increasingly used in strategic decision-making settings, yet evidence shows that, like humans, they often deviate from full rationality. In this study, we compare LLMs and humans using experimental paradigms directly adapted from behavioral game-theory research. We focus on two well-studied strategic games, Rock-Paper-Scissors and the Prisoner's Dilemma, which are well known for revealing systematic departures from rational play in human subjects. By placing LLMs in identical experimental conditions, we evaluate whether their behaviors exhibit the bounded rationality characteristic of humans. Our findings show that LLMs reproduce familiar human heuristics, such as outcome-based strategy switching and increased cooperation when future interaction is possible, but they apply these rules more rigidly and demonstrate weaker sensitivity to the dynamic changes in the game environment. Model-level analyses reveal distinctive architectural signatures in strategic behavior, and even reasoning models sometimes struggle to find effective strategies in adaptive situations. These results indicate that current LLMs capture only a partial form of human-like bounded rationality and highlight the need for training methods that encourage flexible opponent modeling and stronger context awareness.

Black-Box Prompt Optimization: Aligning Large Language Models without Model Training

Large language models (LLMs) have shown impressive success in various applications. However, these models are often not well aligned with human intents, which calls for additional treatments on them, that is, the alignment problem. To make LLMs better follow user instructions, existing alignment methods mostly focus on further training them. However, the extra training of LLMs are usually expensive in terms of GPU compute; worse still, LLMs of interest are oftentimes not accessible for user-demanded training, such as GPTs. In this work, we take a different perspective -- Black-Box Prompt Optimization (BPO) -- to perform alignments. The idea is to optimize user prompts to suit LLMs' input understanding, so as to best realize users' intents without updating LLMs' parameters. BPO is model-agnostic and the empirical results demonstrate that the BPO-aligned ChatGPT yields a 22% increase in the win rate against its original version, and 10% for GPT-4. Importantly, the BPO-aligned LLMs can outperform the same models aligned by PPO and DPO, and it also brings additional performance gains when combining BPO with PPO or DPO. Code and datasets are released at https://github.com/thu-coai/BPO.