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...

We present a complete, separable and metrizable topology on the product space of information and (subjective) beliefs. Such a topology formalizes similarity of differential information without the assumption of a common prior, but under the assumption that objectively impossible events are...

This note illustrates that the saturation property of a probability space can be used to routinely generalize results on the integration of Banach valued correspondences over a Loeb measure space to those over an arbitrary saturated probability space. On the other hand, the saturation property...