GAMES OF INCOMPLETE INFORMATION WITHOUT COMMON KNOWLEDGE PRIORS

We relax the assumption that priors are common knowledge, in the stan-dard model of games of incomplete information. We make the realistic assumption that the players are boundedly rational: they base their ac-tions on finite-order belief hierarchies. When the different layers of beliefs are independent of each other, we can retain Harsányi’s type-space, and we can define straightforward generalizations of Bayesian Nash Equilib-rium (bne) and Rationalizability in our context. Since neither of these concepts is quite satisfactory, we propose a hybrid concept, Mirage Equi-librium, providing us with a practical tool to work with inconsistent belief hierarchies. When the different layers of beliefs are correlated, we must enlarge the type-space to include the parametric beliefs. This presents us with the difficulty of the inherent openness of finite belief subspaces. Appealing to bounded rationality once more, we posit that the players believe that their opponent holds a belief hierarchy one layer shorter than they do and we provide alternative generalizations of bne and Rational-izability. Finally, we show that, when beliefs are degenerate point beliefs, the definition of Mirage Equilibrium coincides with that of the generalized bne. 1 Proem Consider the following simple situation. Bob is competing in a Cournot duopoly with Ann. The two of them produce perfect substitutes at zero cost and compete in quantities. Unfortunately, the demand for their product is not known. There are two demand forecasting agencies in town, offering two different predictions