Before revision:  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 URLers dominance, deemed URLers Rationalizability, and we show that in generic static games both Point Rationalizability and Wald Rationalizability select a subset of the actions selected by URLers Rationalizability. More generally, while we prove that dropping the genericity assumption does not change the relation between Point Rationalizability and URLers Rationalizability, we show that Wald and URLers Rationalizability are not comparable in their behavioral implications, and we shed light on why this difference emerges.
After revision:  While optimism is related to Point Rationalizability, to capture pessimism we introduce 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 genericity assumption does not change the relation between Point Rationalizability and URLers Rationalizability, we show that Wald and URLers Rationalizability are not comparable in their behavioral implications, and we shed light on why this difference emerges.