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 both model 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.