Extreme points of two digraph polytopes: Description and applications in economics and game theory
AbstractIn this paper, we introduce two polytopes that respect a digraph in the sense that for every vector in the polytope every component corresponds to a node and is at least equal to the component corresponding to each successor of this node. The sharing polytope is the set of all elements from the unit simplex that respect the digraph. The fuzzy polytope is the set of all elements of the unit cube respecting the digraph. The main results are characterizations of the extreme points of the above described two digraph polytopes. We also give an economic application of the result on the sharing polytope and a game-theoretical application for the fuzzy polytope.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 44 (2008)
Issue (Month): 11 (December)
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Web page: http://www.elsevier.com/locate/jmateco
Polytope Directed graph Unit simplex Unit cube Core;
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