# On the Aumann–Shapley value

On the Aumann–Shapley value Let L be a D-lattice, i.e. a lattice ordered effect algebra, and let BV be the Banach space of all real-valued functions of bounded variation on L (vanishing at 0) endowed with the variation norm. We prove the existence of a continuous Aumann–Shapley value φ on $$\mathfrak{bv}^\prime$$ NA, the subspace of BV spanned by all functions of the form $$f\circ\mu$$ , where  $$\mu: L \to [0,1]$$ is a non-atomic σ-additive modular measure and $$f: [0,1] \to {\mathbb{R}}$$ is of bounded variation and continuous at 0 and at 1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# On the Aumann–Shapley value

, Volume 12 (4) – May 27, 2008
17 pages

/lp/springer_journal/on-the-aumann-shapley-value-ck0AXt969A
Publisher
SP Birkhäuser Verlag Basel
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-008-2207-x
Publisher site
See Article on Publisher Site

### Abstract

Let L be a D-lattice, i.e. a lattice ordered effect algebra, and let BV be the Banach space of all real-valued functions of bounded variation on L (vanishing at 0) endowed with the variation norm. We prove the existence of a continuous Aumann–Shapley value φ on $$\mathfrak{bv}^\prime$$ NA, the subspace of BV spanned by all functions of the form $$f\circ\mu$$ , where  $$\mu: L \to [0,1]$$ is a non-atomic σ-additive modular measure and $$f: [0,1] \to {\mathbb{R}}$$ is of bounded variation and continuous at 0 and at 1.

### Journal

PositivitySpringer Journals

Published: May 27, 2008

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