Are LLM Agents Exploitable Negotiators ?

Large Language Models (LLMs) have recently demonstrated impressive fluency in strategic and social tasks, including bargaining and negotiation. However, whether such behavior is strategically robust in the game-theoretic sense remains unclear. In this work, we ask a simple but fundamental question: \emph{are LLM-based negotiators exploitable?} We introduce a suite of controlled game-theoretic environments—including auctions, markets, and public goods games—where Nash equilibria are analytically computable. This allows us to move beyond behavioral or payoff-based evaluation and to quantify exploitability by comparing LLM outcomes against equilibrium predictions and against rational and adversarial opponents. Across multiple settings, we find that LLM negotiators systematically deviate from equilibrium: they over-concede, are vulnerable to anchoring and strategic pressure, and frequently generate inefficient outcomes even in simple games. These results show that while LLMs can negotiate fluently, their strategies remain game-theoretically exploitable, highlighting risks for real-world deployment and motivating robustness-oriented training methods such as adversarial training and self-play.