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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 11 (December)
Pages: 1114-1125

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Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1114-1125

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Related research

Keywords: Polytope Directed graph Unit simplex Unit cube Core;

References

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  1. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2007. "Distributing Dividends in Games with Ordered Players," Tinbergen Institute Discussion Papers, Tinbergen Institute 06-114/1, Tinbergen Institute.
  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, Elsevier, vol. 12(1), pages 113-126, January.
  3. Gilles, R.P. & Owen, G. & Brink, J.R. van den, 1991. "Games with permission structures: The conjunctive approach," Discussion Paper, Tilburg University, Center for Economic Research 1991-14, Tilburg University, Center for Economic Research.
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