Abstract
By identifying types whose low-order beliefs - up to level - about the state of nature coincide, we obtain quotient type spaces that are typically smaller than the original ones, preserve basic topological properties, and allow standard equilibrium analysis even under bounded reasoning. Our Bayesian Nash-equilibria capture players' inability to distinguish types belonging to the same equivalence class. The case with uncertainty about the vector of levels is also analyzed. Two examples illustrate the constructions.