René van den Brink () (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam) Gerard van der Laan () (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam) Valeri Vasil'ev () (Sobolev Institute of Mathematics, Novosibirsk, Russia)
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In this paper we describe the extreme points of two closely related polytopes that are assigned to a digraph. The first polytope is the set of all sharing vectors (elements from the unit simplex) such that each node gets at least as much as each of its successors. The second one is the set of all fuzzy vectors (elements of the unit cube) with participation rates of players subordinated to the relationships prescribed by the digraph. We also discuss some applications in cooperative game theory.
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Find related papers by JEL classification: C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General
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