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...

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 [Y.N. Sun, The exact law of large numbers via Fubini extension and characterization of...

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).

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...

This paper studies the existence of pure-strategy Nash equilibria for nonatomic games where players take actions in infinite-dimensional Banach spaces. For any infinite-dimensional Banach space, if the player space is modeled by the Lebesgue unit interval, we construct a nonatomic game which has...

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

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...

In the setting of non-cooperative game theory strategic negligibility of individual agents or diffuseness of information has been modelled as a non-atomic measure space typically the unit interval endowed with Lebesgue measure However recent work has shown that with uncountable action sets as...

We provide a detailed portfolio analysis for a financial market with an atomless continuum of assets. In the context of an exact arbitrage pricing theory (EAPT), we go beyond the characterization of the existence of important portfolios (normalized riskless, mean, cost, factor and mean-variance...