Ambiguity attitudes and self-confirming equilibrium in sequential games

We consider a game in extensive form recurrently played by agents who are randomly drawn from large populations and matched. We assume that preferences over actions at any information set admit a smooth-ambiguity representation in the sense of Klibanoff, Marinacci, and Mukerji (Econometrica, 2005), which may induce dynamic inconsistencies. We take this into account in our analysis of self-confirming equilibrium (SCE) given players' feedback about the path of play. Battigalli, Cerreia-Vioglio, Maccheroni, and Marinacci (Amer. Econ. Rev., 2015) show that the set of SCE's of a simultaneous-move game with feedback expands as ambiguity aversion increases. We show by example that SCE in a sequential game is not equivalent to SCE applied to the strategic form of such game, and that the previous monotonicity result does not extend to general sequential games. Still, we provide sufficient conditions under which the monotonicity result holds for SCE.