Wald's theory of statistical decision functions generalizes statistical estimation and hypotheses testing based upon game theory. Its main theorem is the complete class theorem, one of the earliest results that mathematically justify Bayesian decisions. Although the complete class theorem may appear to be related to Savage's subjective expected utility model, they are quite different in content and purpose. However, we can give an alternative axiomatic foundation for Anscombe and Aumann's subjective expected utility model using the complete class theorem and borrowing ideas from Nakada, Nitzan, Takeoka, and Ui (2020); that is, we can connect Wald's theory to Savage's theory.
