Yeneng Sun

TL;DR: The usual continuum product based on the Kolmogorov construction together with the Lebesgue measure as well as the usual finitely additive measure-theoretic framework is shown to be not suitable for modeling individual risks.

TL;DR: In this article, the existence of pure-strategy Nash equilibria in games with an atomless continuum of players, each with an action set that is not necessarily finite.

TL;DR: In this article, the existence of independent random matching of a large population in both static and dynamic systems has been proved via non-standard analysis, and the proof for the dynamic setting relies on a new Fubini type theorem for an infinite product of Loeb transition probabilities, based on which a continuum of independent Markov chains is derived from random mutation, random partial matching and random type changing.

TL;DR: In this paper, the existence of pure strategy Nash equilibria in nonatomic games was shown by means of counterexamples and the stringent conditions on the cardinality of action sets cannot be relaxed, and thus resolve questions which have remained open since Schmeidler's 1973 paper.

TL;DR: In this paper, the authors provide a measure-theoretic framework for the study of random phenomena involving a large number of economic entities, based on the fact that processes which are measurable with respect to hyperfinite Loeb product spaces capture the limiting behaviors of triangular arrays of random variables and thus constitute the right class for general stochastic modeling.