Decomposition and Characterization of Risk with a Continuum of Random Variables
研究由连续随机变量生成的风险的表示与刻画，将风险分解为总体和特质成分，并用于匿名状态无关支付下的决策问题，最后应用于大博弈模型以描述玩家随机化。
The paper studies the representation and characterization of risks generated by a continuum of random variables. The Main Theorem is a characterization of a broad class of continuum processes in terms of the decomposition of risk into aggregate and idiosyncratic components, and in terms of the approximation of the continuum process by finite collections of random variables. This characterization is used to study decision making problems with anonymous and state-independent payoffs. An Extension Theorem shows that if such a payoff function is defined on simple processes, then it has a unique continuous extension to the class of processes characterized in this paper. This extension is formulated without reference to sample realizations and with minimal restrictions on the patterns of correlation between the random variables. As an application, the theory is used to develop a new model of large games which emphasizes the explicit description of the players' randomizations. This model is used to study the class of environments in which Schmeidler's (1973) representation of strategic uncertainty in large games is valid.