Analysis of information feedback and selfconfirming equilibrium

Recent research emphasizes the importance of information feedback in situations of recurrent decisions and strategic interaction, showing how it affects the uncertainty that underlies selfconfirming equilibrium (e.g., Battigalli et al., 2015, Fudenberg and Kamada, 2015). Here, we discuss in detail several properties of this key feature of recurrent interaction and derive relationships. This allows us to elucidate different notions of selfconfirming equilibrium, showing how they are related to each other given the properties of information feedback. In particular, we focus on Maxmin selfconfirming equilibrium, which assumes extreme ambiguity aversion, and we compare it with the partially-specified-probabilities (PSP) equilibrium of Lehrer (2012). Assuming that players can implement any randomization, symmetric Maxmin selfconfirming equilibrium exists under either “observable payoffs,” or “separable feedback.” The latter assumption makes this equilibrium concept essentially equivalent to PSP-equilibrium. If observability of payoffs holds as well, then these equilibrium concepts collapse to mixed Nash equilibrium.