 Relaxed large economies with infinite-dimensional commodity spaces: The existence of Walrasian equilibriaM. Khan and Nobusumi Sagara Journal of Mathematical Economics, 2016, vol. 67, issue C, 95-107 Abstract: 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 relaxed economies and their 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∞-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. Keywords: Relaxed large economy; Walrasian equilibrium; Saturated measure space; Lyapunov convexity theorem; Purification principle; Relaxed control (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:67:y:2016:i:c:p:95-107 DOI: 10.1016/j.jmateco.2016.09.004 Access Statistics for this article Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii More articles in Journal of Mathematical Economics from Elsevier |
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