Abstract We introduce a novel method of proving existence of rational expectations equilibria (REE) in multi-dimensional CARA-Gaussian environments. Our approach is to construct a mapping from agents’ initial beliefs (which are characterized by a positive semidefinite matrix), to their updated beliefs, after reaching and observing equilibrium; we then show Brouwer’s fixed point theorem applies. We apply our approach to a finite-market version of Admati (1985), which is a multi-asset noisy REE asset pricing model with dispersed information. We present an algorithm to numerically solve for equilibrium of the finite model, as well as several examples illustrating the difference in equilibrium behavior between the finite and infinite models. Our method can be applied to any multi-dimensional REE model with Gaussian uncertainty and behavior that is linear in agents’ information.

中文翻译：

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有限代理，多资产嘈杂理性期望经济中的均衡存在

摘要我们引入了一种新颖的方法，用于证明多维期望CARA-Gaussian环境中存在理性期望均衡（REE）。我们的方法是在达到并观察到均衡之后，构造从代理的初始信念（以正半定矩阵为特征）到其更新的信念的映射。然后，我们证明Brouwer的不动点定理适用。我们将我们的方法应用于Admati（1985）的有限市场版本，该模型是具有分散信息的多资产嘈杂REE资产定价模型。我们提出了一种数值求解有限模型平衡的算法，并提供了一些示例来说明有限模型与无限模型之间平衡行为的差异。