Variational analysis and mathematical economics 1: Subdifferential calculus and the second theorem of welfare economics

The paper consists of two parts. The first is devoted to a general subdifferential theory based on an axiomatic approach. Along with the list of “axioms” which summarizes properties shared by all major subdifferentials studied in variational analysis, we also consider four “optional” properties which specific subdifferentials may or may not have, such as trustworthiness, robustness, tightness (validity of a certain fuzzy subdifferential inequality) and geometric compatibility (connection between subdifferentials and normal cones). The concluding result says that the approximate G-subdifferential is the only subdifferential that has the four properties on all Banach space.

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