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The average tree solution for cooperative games with communication structure
Herings, Peter Jean-Jacques; Laan, Gerard van der; … - 2008
-convexity, under which the game is shown to have a non-empty core and the average tree solution lies in the core. In general, link …
Persistent link: https://www.econbiz.de/10011377055
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Two values for transferable utility games with coalition and graph structure
Brink, René van den; Laan, Gerard van der; Moes, Nigel - 2011
Persistent link: https://www.econbiz.de/10009720713
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Characterizations of Network Power Measures
van den Brink, René; Borm, Peter; Hendrickx, Ruud; … - 2005
A symmetric network consists of a set of positions and a set of bilateral links between these positions. Examples of such networks are exchange networks, communication networks, disease transmission networks, control networks etc. For every symmetric network we define a cooperative transferable...
Persistent link: https://www.econbiz.de/10010325263
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An efficient and fair solution for communication graph games
Brink, René van den; Chmelnitskaja, Anna B.; Laan, … - 2011
We introduce an efficient solution for games with communication graph structures and show that it is characterized by efficiency, fairness and a new axiom called component balancedness. This latter axiom compares for every component in the communication graph the total payoff to the players of...
Persistent link: https://www.econbiz.de/10011386146
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The V L Value for Network Games
Hendrickx, Ruud; Borm, Peter; van den Brink, René; … - 2005
In this paper we consider a proper Shapley value (the V L value) for cooperative network games. This value turns out to have a nice interpretation. We compute the V L value for various kinds of networks and relate this value to optimal strategies in an associated matrix game
Persistent link: https://www.econbiz.de/10014064942
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Cooperative games in graph structure
Herings, Peter Jean-Jacques; Laan, Gerard van der; … - 2000
of ones. We then define the balanced-core as a refinement ofthe core. A payoff vector lies in the balanced-core if it … lies in the core andthe payoff vector is an element of payoff sets of all graphs in some balanced collection ofgraphs. We … prove that any balanced graph game has a nonempty balanced-core.We conclude by some examples showing the usefulness of the …
Persistent link: https://www.econbiz.de/10011303860
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On the extreme points of two polytopes associated with a digraph and applications to cooperative games
Brink, René van den; Laan, Gerard van der; Vasilʹev, … - 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/10011335203
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A strategic implementation of the average tree solution for cycle-free graph games
Brink, René van den; Laan, Gerard van der; Moes, Nigel - 2012
Persistent link: https://www.econbiz.de/10009722639
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Centrality rewarding shapley and Myerson values for undirected graph games
Chmelnitskaja, Anna B.; Laan, Gerard van der; Talman, Dolf - 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/10011531120
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Values for transferable utility games with coalition and graph structure
Brink, René van den; Laan, Gerard van der; Moes, Nigel - In: Top : transactions in operations research 23 (2015) 1, pp. 77-99
Persistent link: https://www.econbiz.de/10010517978