Before revision: We provide a theory of strategic interactions in static games in the presence of ignorance, i.e., when players cannot produce beliefs as probability measures (or similia) concerning the uncertain elements present in the interaction they are involved in. Assuming only players ' ordinal preferences as transparent, we investigate players that are either optimistic or pessimistic, that we deem tropicalplayers. To explicitly formalize these attitudes , we employ tools from interactive epistemology, by defining the corresponding epistemic events in epistemic possibility structures, which are the counterpart of epistemic type structures suited for our analysis in the presence of ignorance, We show that the behavioral implications related to common belief in these events have algorithmic counterparts in terms of iterative deletion procedures.
After revision: We provide a theory of strategic interactions in static games in the presence of ignorance, i.e., when players cannot produce beliefs as probability measures but rather have coarse beliefs represented as subsets of opponents' actions. These players follow either \max \max or \max \min decision criteria. The criteria can be identified as optimistic and pessimistic attitudes, respectively, which we refer to as ``tropical''. Explicitly formalizing these attitudes and how players reason under ignorance, we characterize the behavioral implications related to common belief in these events have algorithmic counterparts in terms of iterative deletion procedures.