Purification results are important in game theory and statistical decision theory. We prove a new purification theorem that generalizes several earlier results. The key idea of our proof is to make use of the exact law of large numbers. As an application, we show that every mixed strategy in...

Purification results are important in game theory and statistical decision theory. The purpose of this paper is to prove a general purification theorem that generalizes many authors' results. The key idea of our proof is to make use of the exact law of large numbers. As an application, we show...

The rational expectations equilibrium (REE), as introduced in Radner (1979) in a general equilibrium setting à la Arrow–Debreu–McKenzie, often fails to have desirable properties such as universal existence, incentive compatibility and efficiency. We resolve those problems by providing a new...

This paper provides a mathematical foundation for independent random matching of a large population, as widely used in the economics literature. We consider both static and dynamic systems with random mutation, partial matching arising from search, and type changes induced by matching. Under...