By circumventing several of the thorny modeling problems in these models, NSA allows the rigorous investigation of the robustness issue to go forward. Professor Stinchcombe has shown that other methods of adding ideal elements, compactification, and finitely additive measures are insufficient, although he and his co-authors have found extensions of games that are sufficient for several large classes of models. NSA and the smaller compactification approach both resolve puzzles in the theory of decision making under uncertainty that have been left open since Savage's foundational work in 1957. The NSA approach also resolves purification puzzles both in cooperative game theory, and in the interpretation of mixed strategy equilibria. The second strand of the theory of games that Professor Stinchcombe researches is the problem of refining the set of equilibria.
Refinement involves finding systematic methods of rejecting equilibria as implausible.
His approach is based on the notion that people are much more certain of their own preferences than they are of the preferences of others. This relative certainty of own preferences leads to a class of perturbations with predictions that are much more palatable than those currently available. Loosely based on some simplified models of the organization of the brain, ANNs are an extremely flexible set of non-linear functional forms. This latter work is partly based on the idea of approximate flatness for infinite dimensional vector spaces, and partly based on considerations of metric entropy. In a purely econometric vein, Professor Stinchcombe has examined the different senses in which stochastic processes that satisfy central limit theorems are dense in the set of all stochastic processes.