This paper analyzes the trust formation, misinformation resistance, and peer input integration capabilities of a large-scale language model (LLM), which is used as a component of collaborative intelligence in multi-agent systems (MAS). Unlike previous studies that primarily focus on groupthink, this paper delves into these aspects, which are crucial for achieving collective intelligence under complex social dynamics. To achieve this, we present KAIROS, a benchmark that simulates a quiz competition with peer agents of varying trust levels, allowing for fine-tuning various conditions such as expert-novice roles, noisy crowds, and adversarial peers. The LLM systematically investigates the impact of trust, peer behavior, and self-confidence on decision-making by collecting both past interactions and current peer responses. We evaluate prompting, supervised learning fine-tuning, and reinforcement learning (GRPO) as mitigation strategies across multiple models. Our results show that GRPO, which combines a multi-agent context, outcome-based rewards, and unconstrained inference, achieves the best performance but is less robust to social influence than the baseline model. The code and dataset are publicly available.