23 research outputs found

    On polyhedral cones of cooperative games

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    Decomposition of Games with Non-empty Core into Veto-Controlled Simple Games

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    The non-negative games with non-empty core form a polyhedral cone. Extreme directions of this convex cone correspond to veto-controlled simple games. In this paper a constructive method is described to represent a non-negative game with non-empty core as a positive linear combination of veto-controlled simple games. As an application a constructive proof is suggested of a result of spinetto (see [5]) dealing with the extreme points of the compact and convex set of nonnegative (0, 1)-normalized games with non-empty core

    On Linear Inequality Systems without Strongly Redundant Constraints

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    For an (m x n)-matrix A the set C(A) is studied containing the constraint vectors b of R(m) without strongly redundant inequalities in the system (Ax less-than-or-equal-to b, x greater-than-or-equal-to 0). C(A) is a polyhedral cone containing as a subset the cone Col(A) generated by the column vectors of A. This paper characterizes the matrices A for which the equality C(A) = Col(A) holds. Furthermore, the matrices A are characterized for which C(A) is generated by those constraint vectors beta(i) is-an-element-of C(A), i is-an-element-of {1, 2, ..., m}, for which the feasible region {x is-an-element-of R+n: Ax less-than-or-equal-to beta(i)} equals {x is-an-element-of R+n: (Ax)i less-than-or-equal-to 1}. Necessary conditions are formulated for a constraint vector to be an element of C(A). The class of matrices is characterized for which these conditions are also sufficient

    Totally Balanced Multi-Commodity Games and Flow Games

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