Identifying higher orders of rationality is crucial to the understanding of strategic behavior. Nonetheless, the identification of a subject's actual order of rationality from observed behavior in games remains highly elusive. Games may significantly impact and hence invalidate the identified order. To tackle this fundamental problem, we introduce an axiomatic approach that singles out a new class of games, the e-ring games. We then present results from a within subject experiment comparing individuals' classification across e-ring games and standard games previously used in the literature. The results show that satisfying the axioms introduced significantly reduces errors and contributes towards a more reliable identification.
