Intentional acquisition of otherwise irrelevant information in general environments

Determine whether intentional acquisition of otherwise irrelevant information by a current self, who anticipates that a future self may acquire additional information, arises in more general environments beyond the case in which the leakage set contains all information structures that are Blackwell more informative than the initially chosen structure.

Background

The paper applies its robust Bayesian persuasion framework to an intrapersonal setting in which a current self selects an information structure while anticipating that a future self may acquire additional information. Because the current self evaluates potential information leakage pessimistically, she may deliberately choose an information structure that reveals information about dimensions—such as whether an underlying ability is good or bad—that are otherwise irrelevant to her preferences.

The paper notes that Kitano (2026) establishes this behavior in a particular environment where the leakage set contains every information structure that is Blackwell more informative than the selected structure. The unresolved issue is whether the same intentional acquisition of otherwise irrelevant information persists under more general specifications of the leakage set or other environments.