Heterogeneously perceived incentives in dynamic environments: rationalization, robustness and unique selections (joint with E. Piermont (Royal Holloway – University of London)); Peio Zuazo-Garin (HSE University)

We consider dynamic interactions with payoff-uncertainty where common knowledge about the limits of how information may be updated is relaxed. More specifically, we model players as endowed with a subjective hierarchy of state-spaces that represents the state-space they update their beliefs in, the state-space they consider others to update their beliefs in, and so on. We compare the robustness of forward and backward induction versions of rationalizability (embodied by strong and backward rationalizability, respectively) to perturbations of these hierarchies and find that: (1) backward induction predictions are robust in the whole space of hierarchies; (2) while forward induction predictions display failures of upper-hemicontinuity, they are robust in a generic subset of the space of hierarchies; (3) in an open set generically containing the hierarchies that represent the benchmark case of a commonly known state-space, forward induction predictions are generically unique (c.f. Weinstein and Yilidiz, even around the hierarchies based on state-spaces that do not satisfy richness assumptions; (4) arbitrarily \textit{small} heterogeneity on the hierarchies of state-spaces across players suffices to invalidate the classic insight that forward induction predictions refine backward induction ones.