Games of incomplete information without common knowledge priors

We relax the assumption that priors are common knowledge, in the standard m odel of games of incomplete information. We make the realistic assumption t hat the players are boundedly rational: they base their actions on finite-o rder belief hierarchies. When the different layers of beliefs are independe nt of each other, we can retain Harsanyi's type-space, and we can define st raightforward generalizations of Bayesian Nash Equilibrium (BNE) and Ration alizability in our context. Since neither of these concepts is quite satisf actory, we propose a hybrid concept, Mirage Equilibrium, providing us with a practical tool to work with inconsistent belief hierarchies. When the dif ferent 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 rationa lity once more, we posit that the players believe that their opponent holds a belief hierarchy one layer shorter than they do and we provide alternati ve generalizations of BNE and Rationalizability. Finally, we show that, whe n beliefs are degenerate point beliefs, the definition of Mirage Equilibriu m coincides with that of the generalized BNE.