Inference-time computation is a critical yet challenging paradigm for enhancing the reasoning performance of large language models (LLMs). While existing strategies improve reasoning stability and consistency, they suffer from notable limitations: self-correction often reinforces the model’s initial biases, and Multi-Agent Collaboration (MAC) often fails due to the lack of efficient coordination mechanisms, leading to collective errors. Although high-performing verifiers can detect reasoning errors, making them reliable requires substantial training. To address these challenges, we introduce a novel inference-time framework - **Adaptive Coopetition (AdCo)** - in which LLM agents utilize **an adaptive, UCB-based ‘coopetition’ mechanism**. At each round, agents leverage coarse verifier signals to determine whether to collaborate or compete, further iteratively refining their reasoning based on peer feedback. Without relying on high-performance verifiers, our adaptive strategy achieves significant performance gains on mathematical reasoning benchmarks, yielding **a 20% relative improvement** over baselines on the more challenging dataset. Our approach remains robust and consistent in terms of accuracy under different sample sizes and configurations. This adaptive, signal-guided ‘coopetition’ framework enhances reasoning robustness by leveraging bothmodel knowledge diversity and reasoning trace measure, while also promoting uncertainty-driven exploration, especially when participants have comparable capabilities. From this perspective, our work offers a fresh lens on inference-time computation and paves the way for more resilient multi-agent LLM systems.