We test the portability of level‐0 assumptions in level‐k theory in an experimental investigation of behavior in Coordination, Discoordination, and Hide and Seek games with common, non‐neutral frames. Assuming that level‐0 behavior depends only on the frame, we derive hypotheses that are independent of prior assumptions about salience. Those hypotheses are not confirmed. Our findings contrast with previous research which has fitted parameterized level‐k models to Hide and Seek data. We show that, as a criterion of successful explanation, the existence of a plausible model that replicates the main patterns in these data has a high probability of false positives.