On the Extreme Points of Two Polytopes associated with a Digraph and Applications to Cooperative Games

Rene van den Brink (), Gerard van der Laan and Valery Vasil'ev ()

No 04-069/1, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: See also the publication in 'Journal of Mathematical Economics', 2008, 44, 1114-1125.

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.

Keywords: polytope; directed graph; unit simplex; unit cube; cooperate game (search for similar items in EconPapers)
JEL-codes: C60 C71 (search for similar items in EconPapers)
Date: 2004-06-15
References: Add references at CitEc
Citations: View citations in EconPapers (1)

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