Interim partially correlated rationalizability

We formalize a solution concept called interim partially correlated rationalizability (IPCR), which was implicitly discussed in both Ely and Peski (2006) and Dekel et al. (2007). IPCR allows for interim correlations, i.e., correlations that depend on opponents' types but not on the state of nature. As a direct extension of Ely and Peski's main result, we show that hierarchies of beliefs over conditional beliefs are necessary and sufficient for the identification of IPCR. We use new proof techniques that better illustrate the connection between higher order beliefs and interim rationalizability.