Opponent Shaping in LLM Agents

Abstract: LLMs are increasingly being deployed as autonomous agents in real-world environments. As these deployments scale, multi-agent interactions become inevitable, making it essential to understand strategic behavior in such systems. A central open question is whether LLM agents, like reinforcement learning agents, can shape the learning dynamics and influence the behavior of others through interaction alone. In this paper, we present the first investigation of opponent shaping (OS) with LLM-based agents. Existing OS algorithms cannot be directly applied to LLMs, as they require higher-order derivatives, face scalability constraints, or depend on architectural components that are absent in transformers. To address this gap, we introduce ShapeLLM, an adaptation of model-free OS methods tailored for transformer-based agents. Using ShapeLLM, we examine whether LLM agents can influence co-players' learning dynamics across diverse game-theoretic environments. We demonstrate that LLM agents can successfully guide opponents toward exploitable equilibria in competitive games (Iterated Prisoner's Dilemma, Matching Pennies, and Chicken) and promote coordination and improve collective welfare in cooperative games (Iterated Stag Hunt and a cooperative version of the Prisoner's Dilemma). Our findings show that LLM agents can both shape and be shaped through interaction, establishing opponent shaping as a key dimension of multi-agent LLM research.