商品空间为Infinite-Dimensional的松弛大经济：瓦尔拉斯均衡的存在性
Relaxed Large Economies with Infinite-Dimensional Commodity Spaces: The Existence of Walrasian Equilibria
摘要：
虽然“聚合凸化”在数理经济学中是一个很好理解的过程，但“随机凸化”在很大程度上仅限于统计决策、最优控制和非合作对策的理论。在本文中，在经典的瓦尔拉斯一般均衡理论的背景下，我们提供了一个全面的治疗{ \it松弛经济}和他们的{ \it松弛瓦尔拉斯均衡}：我们的结果涉及到一个有限的或连续的代理设置，以及连续的商品建模为一个有序的可分巴拿赫空间或作为一个$L^\infty$ -空间。作为一个实质性的结果，我们证明，凸性假设可以从原来的大经济体的饱和假设下，现有的结果可以毫不费力地恢复。
英文摘要：
Whereas "convexification by aggregation" is a well-understood procedure in mathematical economics, "convexification by randomization" has largely been limited to theories of statistical decision-making, optimal control and non-cooperative games. In this paper, in the context of classical Walrasian general equilibrium theory, we offer a comprehensive treatment of {\it relaxed economies} and their {\it relaxed Walrasian equilibria}: our results pertain to a setting with a finite or a continuum of agents, and a continuum of commodities modeled either as an ordered separable Banach space or as an $L^\infty$-space. As a substantive consequence, we demonstrate that the convexity hypothesis can be removed from the original large economy under the saturation hypothesis, and that existing results in the antecedent literature can be effortlessly recovered.
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