Drivers of LLM Consensus Formation Under Competing Incentives: A Simulation Study

Large Language Models (LLMs) are increasingly deployed in multi-agent environments that produce unanimous agreement, both in intended interactions that need coordination and in unintended emergent interactions. Consequently, understanding how LLMs with competing incentives reach consensus is crucial to better interpret and design LLM collectives. We introduce an evaluation, based on the Network Consensus game, to assess the mechanisms driving this process. Here, a network of agents must agree on one of two colours to receive a payoff, but agents are offered different payoffs for the agreed colour. We vary components such as communication access and network structure and assess six open-source models and one closed model (ChatGPT 5.6-sol). We find that open-source LLMs reach consensus less often than humans in comparable experiments and only if messages are communicated across the global network. ChatGPT 5.6-sol, however, is able to reach consensus with communication limited to its neighbours and with no communication ability. This is achieved through lower stubbornness and higher majority-following tendencies, and by providing more information about its neighbours' states in messages. However, situating agents in a highly clustered graph reduces consensus, regardless of these traits, demonstrating that both system design and individual model traits drive collective outcomes.