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This paper studies the strategic reasoning in a static game played betweenheterogeneous populations. Each population has representative preferences witha random variable indicating individuals' idiosyncrasies. By assumingrationality, common belief in rationality, and the transparency that players'beliefs are consistent with the distribution p of the idiosyncrasies, we apply$\Delta$-rationalizability (Battigalli and Siniscalchi, 2003) and deduce anempirically testable property of population behavior called$\Delta^{p}$-rationalizability. We show that every action distributiongenerated from a quantal response equilibrium (QRE, McKelvey and Palfrey, 1995)is $\Delta^{p}$-rationalizable. We also give conditions under which theconverse is true, i.e., when the assumptions provide an epistemic foundationfor QRE and make it the robust prediction of population behavior.

Rationalization, Quantal Response Equilibrium, and Robust Action Distributions in Populations