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A common experimental research design is one in which individuals are randomly assigned to groups, and then groups interact under different treatment conditions (e.g., a game structure). We present methods for design-based inference for such ``group interaction'' experiments. A key consideration is that group interaction experiments intentionally introduce forms of interference, which yields dependencies that should be accounted for when making inferential claims. We present results for average treatment effects and derive implications for inferential practice, including potential biases from using conventional cluster robust variance estimators.