Going Beyond the Traditional Possibility Correspondence Model : The Empty Information Set in Recognition Correspondence Model

This note introduces a new model, termed recognition correspondence, which accounts for situations where agents fail to recognize signals, affecting their decision-making. In contrast with traditional possibility correspondence, this model addresses both technical and cognitive limitations that lead to empty information sets. These sets, interpreted as the absence of sensory signals, prevent agents from recalling or updating knowledge. Market behavior during the subprime mortgage crisis and asymptomatic COVID-19 infection illustrates the model. We also redefine the knowledge operator within this framework and explore its implications for non-trivial unawareness. The model demonstrates that, even when agents receive no signals, they default to habitual behavior rather than conscious decision-making.