2016/06/06 by M. Ali Khan, Khan, M. Ali, Nobusumi Sagara +1 · 1 citation
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Economic Theory and Policy #Economic theories and models #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1606.01648
openalex publication_date 2016/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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^∞-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.