Implicit Smooth Ambiguity: Perception, Attitude, and Identification

This paper develops a model of identifiable smooth ambiguity in a finite-state Anscombe-Aumann framework in which ambiguity perception and the ambiguity-attitude representation may depend on the act's endogenous certainty-equivalent utility level. The framework separates two sources of utility-level dependence that standard smooth-ambiguity models hold fixed. Neutral-transfer experiments within revealed cells recover conditional beliefs, while compensation experiments across cells recover cell weights and locally revealed ambiguity-attitude scales. These objects have distinct behavioral content. After the within-level structure is extended globally, ambiguity perception is identified at each certainty-equivalent level, whereas variation in admissible level-specific global attitude indices need not by itself reflect behaviorally identified variation in ambiguity attitude. Cross-level restrictions determine when the locally revealed attitude scales can instead be represented by one common global ambiguity-attitude index. The baseline characterization yields a doubly implicit smooth-ambiguity representation with level-specific perception and potentially level-specific global attitude indices. Requiring one common ambiguity-attitude index gives an intermediate stable-attitude model in which only perception may vary; imposing perception stability as well yields standard identifiable smooth ambiguity within the maintained full-support, neutrally separated, fixed-partition environment with at least three revealed cells. The contribution is therefore a behavioral decomposition of utility-level dependence in smooth ambiguity into separately revealed perception and attitude components.