Saturation and Economic Theory

Abstract

In this dissertation, we report on fruitful applications of the theory of saturated probability spaces developed by Hoover and Keisler (1984) into economic theory, as poineered by Keisler and Sun (2009). First, a rich Fubini extension is constructed on an extension of the Lebesgue unit interval. Second, we prove a new purification theorem based on saturated probability spaces that generalizes several earlier results. Third, for private information games, we show that the saturation property provides a sufficient and necessary framework to model private information in the sense that there exists a pure strategy Nash equilibrtium for such games. Finally, we present a new perspective to understand the necessity of the saturation property in terms of Lebesgue extensions.