Humans Expect Rationality From LLM Opponents in Games

A monetarily-incentivized laboratory experiment compared individual human play in a multi-player p-beauty contest against other humans and against Large Language Models (LLMs). The authors find humans choose significantly lower numbers when facing LLMs, driven by a higher rate of the zero Nash-equilibrium choice. The effect is strongest among subjects with high strategic reasoning ability, who explicitly cite perceived LLMs reasoning and an unexpected perceived propensity for cooperation.

The study uses a within-subject design to compare each participant's choices across human-opponent and LLM-opponent conditions. Key empirical findings include:

• •A statistically significant downward shift in chosen numbers when opponents are LLMs versus humans.
• •A larger incidence of the zero Nash-equilibrium choice in the LLM condition.
• •Heterogeneity: high-strategic-reasoning subjects account for most of the shift and motivate choices by beliefs about LLMs reasoning and cooperation.

This is one of the first controlled, incentivized experiments probing strategic human behavior against modern language models. The results speak directly to deployment settings where algorithmic agents act as opponents, partners, or contract bidders. Expectation shifts and belief heterogeneity can alter equilibrium outcomes, efficiency, and welfare in markets and games that mix humans and AI.

• •Mechanism design must account for altered human best responses to algorithmic agents; traditional equilibria may not predict mixed human-AI systems.
• •Evaluation of multi-agent systems should include behavioral lab tests, not only synthetic self-play or ML benchmarks.
• •User modeling and interface signalling matter: perceived reasoning and cooperation drive behavior and can be modulated by agent transparency.

Validate these findings across other strategic games, different LLM prompting regimes, and real-world field settings. Designers should experiment with agent transparency and incentives to avoid unintended strategic distortions.