On the dimensionality of bounds generated by the Shapley–Folkman theorem

B-Tier
Journal: Journal of Mathematical Economics
Year: 2012
Volume: 48
Issue: 1
Pages: 59-63

Score contribution per author:

2.011 = (α=2.01 / 1 authors) × 1.0x B-tier

α: calibrated so average coauthorship-adjusted count equals average raw count

Abstract

The Shapley–Folkman theorem places a scalar upper bound on the distance between a sum of non-convex sets and its convex hull. We observe that some information is lost when a vector is converted to a scalar to generate this bound and propose a simple normalization of the underlying space which mitigates this loss of information. As an example, we apply this result to the Anderson (1978) core convergence theorem, and demonstrate how our normalization leads to an intuitive, unitless upper bound on the discrepancy between an arbitrary core allocation and the corresponding competitive equilibrium allocation.

Technical Details

RePEc Handle
repec:eee:mateco:v:48:y:2012:i:1:p:59-63
Journal Field
Theory
Author Count
1
Added to Database
2026-01-29