Quotient spaces of boundedly rational types - Davide Cianciaruso; Fabrizio Germano (Northwestern University, Kellogg School of Management, Center for Mathematical Studies in Economics and Management Science, 2011)
By identifying types whose low-order beliefs - up to level li - 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 (li, l-i)-equilibria capture players' inability to distinguish types belonging to the same equivalence class. The case with uncertainty about the vector of levels (li, l-i) is also analyzed. Two examples illustrate the constructions.
Keywords: C72; D03; D83; 330; incomplete-information games; high-order reasoning; type space; quotient space; hierarchies of beliefs; bounded rationality