Subjective contingencies and limited Bayesian updating

We depart from Savage's (1954) common state space assumption and introduce a model that allows for a subjective understanding of uncertainty. Within the revealed preference paradigm, we take the analyst's perspective and uniquely identify the agent's subjective state space via her preferences conditional on incoming information. According to our representation, the agent's subjective contingencies correspond to sets of the analyst's states and, as such, are coarse. The agent uses an additively separable utility with respect to her set of contingencies; and she adopts an updating rule that follows the Bayesian spirit but is limited by her perception of uncertainty. We illustrate the relevance of our theory with applications to the confirmatory bias and correlation neglect, as well as to optimal contract design.