Extreme Points of Two Digraph Polytopes: Description and Applications in Economics and Game Theory

J.R. van den Brink, G. van der Laan, V. Vasil'ev

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    Abstract

    In 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. © 2008 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)1114-1125
    JournalJournal of Mathematical Economics
    Volume44
    DOIs
    Publication statusPublished - 2008

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