This paper presents a new contribution to the growing set of benchmarks used to prune potential AI designs. Much as one might evaluate a machine in terms of its performance at chess, this benchmark involves testing a machine in terms of its performance at a game called "Musical Chairs." At the time of writing, Claude, ChatGPT, and Qwen each failed this test, so the test could aid in their ongoing improvement. Furthermore, this paper sets a stage for future innovation in game theory and AI safety by providing an example of success with non-standard approaches to each: studying a game beyond the scope of previous game theoretic tools and mitigating a serious AI safety risk in a way that requires neither determination of values nor their enforcement.

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