Making decisions under model misspecification

We use decision theory to confront uncertainty that is sufficiently broad to incorporate "models as approximations." We presume the existence of a featured collection of what we call "structured models" that have explicit substantive motivations. The decision maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend the max-min analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision-making are simplified approximations. Formally, we provide an axiomatic rationale for a decision criterion that incorporates model misspecification concerns. We then extend our analysis beyond the max-min case allowing for a more general criterion that encompasses a Bayesian formulation.