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...

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 theory of large one-shot simultaneous-play games with a biosocial typology has been presented in both the individualized and distributionalized forms-large individualized games (LIG) and large distributionalized games (LDG), respectively. Using an example of an LDG with two actions and a...

We study the trade-off between stability and students' welfare in school choice problems. We call a matching weakly stable if none of its blocking pairs can be matched in a more stable matching–one with a weakly smaller set of blocking pairs. A matching is said to be self-constrained efficient...

We propose a notion of core for school choice problems. We say that a coalition of students is able to enforce a subassignment among them if, given their priorities at schools, other students together cannot exclude any of them from her assignment. An assignment is in the core if no coalition of...

For school choice (priority-based allocation) problems, when the priority structure is acyclic, the associated student-proposing deferred acceptance algorithm is Pareto efficient and group strategy-proof (Ergin, 2002). We reveal a hidden iterative removal structure behind such deferred...

Many economic models include random shocks imposed on a large number (continuum) of economic agents with individual risk. In this context, an exact law of large numbers and its converse is presented in Sun (2006) to characterize the cancelation of individual risk via aggregation. However, it is...

The theory of large one-shot simultaneous-play games with a biosocial typology has been presented in both the individualized and distributionalized forms-large individualized games (LIG) and large distributionalized games (LDG), respectively. Using an example of an LDG with two actions and a...