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...

This paper reports a definitive resolution to the question of the existence of a pure-strategy Bayesian–Nash equilibrium in games with a finite number of players, each with a compact metric action set and private information. The resolution hinges on saturated spaces. If the individual spaces...

A comprehensive theory of large strategic games with (socioeconomic and biological) traits (LSGT) has recently been presented in Khan et al. (2012, 2013), and we present a reformulation pertaining to large distributional games with traits (LDGT).