Assuming only ordinal preferences as transparent, we study players interacting under the veil of ignorance, that 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: while optimism is related to Point Rationalizability, a new algorithm—Wald Rationalizability—captures pessimism. Our characterizations allow us to uncover novel connections and results: (i) regarding optimism, we prove that dropping the (implicit) assumption that whatever a player believes is also true allows to capture wishful thinking á la Yildiz (2007), thus reversing an existence failure described therein; (ii) by studying how pessimism and optimism relate to Börgers dominance, we shed light on the appropriate notion of rationality in ordinal games; (iii) finally, with respect to pessimism, our analysis identifies Wald Rationalizability as the limit point of players becoming infinitely risk averse, hence, clarifying the conceptual underpinnings behind a discontinuity in the analysis of Rationalizability in presence of varying risk attitudes hinted in Weinstein (2016).
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