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Generalization of Binomial Coeffi cients to Numbers on the Nodes of Graphs

Khmelnitskaya, Anna - 2016

The triangular array of binomial coefficients, or Pascal's triangle, is formed by starting with an apex of 1. Every row of Pascal's triangle can be seen as a line-graph, to each node of which the corresponding binomial coefficient is assigned. We show that the binomial coefficient of a node is...

Persistent link: https://www.econbiz.de/10012998942

Centrality Rewarding Shapley and Myerson Values for Undirected Graph Games

Khmelnitskaya, Anna - 2016

In this paper we introduce two values for cooperative games with communication graph structure. For cooperative games the shapley value distributes the worth of the grand coalition amongst the players by taking into account the worths that can be obtained by any coalition of players, but does...

Persistent link: https://www.econbiz.de/10012983828

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

van den Brink, René; van der Laan, Gerard; Vasil'ev, … - 2004

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...

Persistent link: https://www.econbiz.de/10014029186

Centrality Rewarding Shapley and Myerson Values for Undirected Graph Games

Khmelnitskaya, Anna - 2020

Persistent link: https://www.econbiz.de/10012855179

An Algorithm for Computing the Nucleolus of Disjunctive Additive Games with An Acyclic Permission Structure

van den Brink, René; Katsev, Ilya; van der Laan, Gerard - 2008

-called peer group games being non-negative additive games on a permission tree. We provide a polynomial time algorithm for …

Persistent link: https://www.econbiz.de/10010325798

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

van den Brink, René; van der Laan, Gerard; Vasil'ev, Valeri - 2004

Persistent link: https://www.econbiz.de/10010325211

A Strategic Implementation of the Average Tree Solution for Cycle-Free Graph Games

van den Brink, Rene; van der Laan, Gerard; Moes, Nigel - 2012

In this note we provide a strategic implementation of the average tree solution for zero-monotonic cycle-free graph games. That is, we propose a non-cooperative mechanism of which the unique subgame perfect equilibrium payoffs correspond to the average hierarchical outcome of the game. This...

Persistent link: https://www.econbiz.de/10010326336

Solving Discrete Systems of Nonlinear Equations

van der Laan, Gerard; Talman, Dolf; Yang, Zaifu - 2009

prove this we use a simplicial algorithm that terminates with a zero point within a finite number of iterations. The …

Persistent link: https://www.econbiz.de/10010325776

Computing Integral Solutions of Complementarity Problems

van der Laan, Gerard; Talman, Dolf; Yang, Zaifu - 2005

In this paper an algorithm is proposed to find an integral solution of (nonlinear) complementarity problems. The … algorithm starts with a nonnegative integral point and generates a unique sequence of adjacent integral simplices of varying … dimension. Conditions are stated under which the algorithm terminates with a simplex one of whose vertices is an integral …

Persistent link: https://www.econbiz.de/10010325585

Computation of the Nucleolus for a Class of Disjunctive Games with a Permission Structure

van den Brink, René; Katsev, Ilya; van der Laan, Gerard - 2008

provide a polynomial time algorithm for computing the nucleolus of the restricted games corresponding to a class of games with …

Persistent link: https://www.econbiz.de/10010325689