  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
tropical players. 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. While
optimism is related to Point Rationalizability, to capture pessimism we
introduce a new algorithm, deemed Wald Rationalizability. We show that the
algorithmic procedure capturing optimism selects a subset of the strategies
selected by the algorithmic procedure capturing pessimism. Additionally, we
compare both algorithmic procedures to an analogous algorithm based on
B\"orgers dominance, deemed B\"orgers Rationalizability, and we show that in
generic static games both Point Rationalizability and Wald Rationalizability
select a subset of the actions selected by B\"orgers Rationalizability. More
generally, while we prove that dropping the genericity assumption does not
change the relation between Point Rationalizability and B\"orgers
Rationalizability, we show that Wald and B\"orgers Rationalizability are not
comparable in their behavioral implications, and we shed light on why this
difference emerges. Finally, we explore connections to strategic wishful
thinking.
