Existing evaluations of large language models primarily rely on single-agent dilemmas or static binary-choice tasks, offering limited insight into how cooperation contexts influence LLM behavior. We introduce CoopValue, a multi-agent evaluation framework that assesses LLMs’ value preferences through cooperative scenarios. CoopValue includes 1,778 scenarios spanning all pairwise conflicts among the 10 Schwartz values and three cooperation types: reciprocal, coopetitive, and altruistic. We evaluate 24 LLMs across 8 model families and examine how their value preferences vary across different cooperative contexts, showing the importance of assessing LLM value preferences in interactive, context-sensitive settings to guide the selection and deployment of LLMs aligned with desired cooperative behavior.