A core challenge for autonomous LLM agents in collaborative settings is balancing robust privacy understanding and preservation alongside task efficacy. Existing privacy benchmarks only focus on simplistic, single-turn interactions where private information can be trivially omitted without affecting task outcomes. In this paper, we introduce MAGPIE (Multi-AGent contextual PrIvacy Evaluation), a novel benchmark of 200 high-stakes tasks designed to evaluate privacy understanding and preservation in multi-agent collaborative, non-adversarial scenarios. MAGPIE integrates private information as essential for task resolution, forcing agents to balance effective collaboration with strategic information control. Our evaluation reveals that state-of-the-art agents, including GPT-5 and Gemini 2.5-Pro, exhibit significant privacy leakage, with Gemini 2.5-Pro leaking up to 50.7% and GPT-5 up to 35.1% of the sensitive information even when explicitly instructed not to. Moreover, these agents struggle to achieve consensus or task completion and often resort to undesirable behaviors such as manipulation and power-seeking (e.g., Gemini 2.5-Pro demonstrating manipulation in 38.2% of the cases). These findings underscore that current LLM agents lack robust privacy understanding and are not yet adequately aligned to simultaneously preserve privacy and maintain effective collaboration in complex environments.