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Extreme points of two digraph polytopes: Description and applications in economics and game theory

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  • van den Brink, René
  • van der Laan, Gerard
  • Vasil'ev, Valeri

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.

Suggested Citation

  • van den Brink, René & van der Laan, Gerard & Vasil'ev, Valeri, 2008. "Extreme points of two digraph polytopes: Description and applications in economics and game theory," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1114-1125, December.
  • Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1114-1125
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    References listed on IDEAS

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    1. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    2. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
    3. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 23-38.
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