Abstract: Most traditional digital games are little concerned about the description of high-level dynamic interactions, and do not support describing collaboration relations and planning of multi-level of groups. Furthermore, few of them are based on a complete formal theory. The description logic of tasks combines the knownlege representation structure of the description logic and the task semantics of the logic of tasks. A formal definition of the collaboration and collaborative planning in digital games is provided, which defines the completeness of the task. Meanwhile, a decision theorem of the completeness of the planning under joint strategies is also given by the method. Experimental results demonstrate that task interaction semantics in high-level relationship of the virtual group is described accurately, and decidable deduction service for the completeness of the collaborative planning is provided as well.