When Numbers Start Talking: Numerical Signalling and Strategic Behaviour Among LLMs

Large language model (LLM) agents are increasingly deployed in competitive multi-agent settings, raising fundamental questions about whether they converge to equilibria and how their strategic behavior can be characterized. In this paper, we study LLM agent interactions in two standard games: a network resource allocation game and a Cournot competition game. Rather than converging to Nash equilibria, we find that LLM agents tend to cooperate when given multi-round prompts and non-zero-sum context. Chain-of-thought analysis reveals that fairness reasoning is central to this behavior. We propose an analytical framework that captures the dynamics of LLM agent reasoning across rounds and explains these experimental findings.

As LLM-based agents with user-instructed goals are becoming widely deployed, they increasingly encounter each other in strategic interactions, and face challenges of finding mutually beneficial outcomes. Prior literature has argued that cooperation problems such as the Prisoner's Dilemma are resolvable in settings where agents know they follow very similar decision making patterns, as for example in monocultural AI ecosystems. Following that line of work, this paper introduces the first framework for evaluating LLM decision making when agents are provided with graded similarity signals. Among our findings, we establish that different LLM models vary drastically in how they navigate similarity signals, with some modern models showing consistent behavior across cooperation problems, payoff structures, and prompt framing. Perhaps surprisingly, our experiments also show that the dataset based on which the similarity signal is computed has small to no impact on induced cooperation, and that LLM models systematically self-identify as highly similar when asked to evaluate another model's chain-of-thought reasoning by themselves. Finally, we develop an LLM-behavioral-game-theoretic model that captures some of their reasoning rationale, and show that it can support cooperative outcomes in equilibrium under sufficiently high similarity scores.

Large language model (LLM) agents increasingly coordinate in multi-agent systems, yet we lack an understanding of where and why cooperation fails. Many real-world coordination problems are not social dilemmas: helping others -- sharing documentation, unblocking a teammate -- costs the helper almost nothing while producing substantial collective benefit. Whether LLM agents cooperate in this regime, where helping is free and they are explicitly instructed to do so, remains unknown. We build a turn-based multi-agent environment that strips away all strategic complexity, making cooperation costless and trivially optimal. Across eight widely used LLMs, capability does not predict cooperation: OpenAI o3 reaches only 17% of optimal collective performance while the weaker o3-mini reaches 50%, despite identical instructions to maximize group revenue. Using a causal decomposition that automates one side of agent communication, we separate cooperation failures from competence failures, and find that several capable models actively withhold information despite gaining nothing from withholding. Targeted interventions address each mode: explicit protocols roughly double the performance of competence-limited models, while small sharing incentives unlock cooperation-limited ones. Our results suggest that scaling intelligence alone will not solve coordination in multi-agent systems, and will require deliberate cooperative design, even when helping costs nothing.