  We study players interacting under the veil of ignorance, who have -- coarse
-- beliefs represented as subsets of opponents' actions. We analyze when these
players follow $\max \min$ or $\max\max$ decision criteria, which we identify
with pessimistic or optimistic attitudes, respectively. Explicitly formalizing
these attitudes and how players reason interactively under ignorance, we
characterize the behavioral implications related to common belief in these
events: while optimism is related to Point Rationalizability, a new algorithm
-- Wald Rationalizability -- captures pessimism. Our characterizations allow us
to uncover novel results: ($i$) regarding optimism, we relate it to wishful
thinking \'a la Yildiz (2007) and we prove that dropping the (implicit)
"belief-implies-truth" assumption reverses an existence failure described
therein; ($ii$) we shed light on the notion of rationality in ordinal games;
($iii$) we clarify the conceptual underpinnings behind a discontinuity in
Rationalizability hinted in the analysis of Weinstein (2016).
