How LLMs Reshape Equilibrium: A Study of Human-AI Competition in Auctions

With the rapid development of AI technologies, LLM agents are increasingly deployed as autonomous decision-makers in economic contexts, rather than merely as advisory tools. This shift fosters human-AI synthetic environments, in which human decision-makers interact and compete with LLM agents. Economists have developed an equilibrium framework to understand and predict human strategies and to guide mechanism design. However, whether this equilibrium framework continues to apply in human-AI synthetic competitive environments remains an open question. To this end, we conduct a series of common-value auction experiments, in which simulation agents and equilibrium agents are used to model human bidders interacting with LLM agents. Using descriptive comparisons and mixed-effects model analyses, we find that LLM agents' bidding strategies (ChatGPT and DeepSeek) exhibit systematic deviations from equilibrium bidding. At high-valuation levels, aggressive bids lead LLM agents to suffer from the winner's curse, despite some degree of bid shading. In contrast, both LLM agents exhibit limited sensitivity to underestimation at low-valuation levels. Further, learning effect from historical outcome feedback can mitigate the severity of the winner's curse. Importantly, when facing LLM opponents, Nash equilibrium strategies may no longer constitute optimal responses, particularly when LLM agents adopt aggressive bidding strategies. Moreover, auction scale and valuation uncertainty further undermine the optimality of equilibrium. These findings also suggest that organizers may need to move beyond mechanism design approaches based solely on equilibrium predictions.