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Two Values for Transferable Utility Games with Coalition and Graph Structure
van den Brink, René - 2011
In this paper we introduce and characterize two new values for transferable utility games with graph restricted communication and a priori unions. Both values are obtained by applying the Shapley value to an associated TU-game. The graph-partition restricted TU-game is obtained by taking the...
Persistent link: https://www.econbiz.de/10013118315
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The Average Tree Solution for Cooperative Games with Communication Structure
Herings, P. Jean-Jacques - 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/10012723255
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Games on Union Closed Systems
van den Brink, René; Katsev, Ilya V.; van der Laan, Gerard - 2011
coalitions also their union is feasible. Properties of solutions (the core, the nucleolus, the prekernel and the Shapley value …
Persistent link: https://www.econbiz.de/10014044020
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Multi-Player Agents in Cooperative TU-Games
van den Brink, René - 2012
A situation in which a finite set of agents can generate certain payoffs by cooperation can be described by a cooperative game with transferable utility (or simply a TU-game) where each agent is represented by one player in the game. In this paper, we assume that one agent can be represented by...
Persistent link: https://www.econbiz.de/10013113020
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Comparable Axiomatizations of the Myerson Value, the Restricted Banzhaf Value, Hierarchical Outcomes and the Average Tree Solution for Cycle-Free Graph Restricted Games
van den Brink, René - 2009
We consider cooperative transferable utility games, or simply TU-games, with a limited communication structure in which players can cooperate if and only if they are connected in the communication graph. A difference between the restricted Banzhaf value and the Myerson value (i.e. the Shapley...
Persistent link: https://www.econbiz.de/10014200526
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Efficiency and Collusion Neutrality of Solutions for Cooperative TU-Games
van den Brink, René - 2009
Three well-known solutions for cooperative TU-games are the Shapley value, the Banzhaf value and the equal division solution. In the literature various axiomatizations of these solutions can be found. Axiomatizations of the Shapley value often use efficiency which is not satisfied by the Banzhaf...
Persistent link: https://www.econbiz.de/10014206096
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The Balanced Solution for Cooperative Transferable Utility Games
van den Brink, René; Levinsky, Rene; Zeleny, Miroslav - 2007
The Shapley value of a cooperative transferable utility game distributes the dividend of each coalition in the game equally among its members. Given exogenous weights for all players, the corresponding weighted Shapley value distributes the dividends proportionally to their weights. In this...
Persistent link: https://www.econbiz.de/10014048251
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Axiomatization and Implementation of Discounted Shapley Values
van den Brink, René; Funaki, Yukihiko - 2010
We generalize the null player property (satisfied by the Shapley value) and nullifying player property (satisfied by the equal division solution) to the so-called delta-reducing player property, stating that a delta-reducing player (being a player such that any coalition containing this player...
Persistent link: https://www.econbiz.de/10014045005
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Axiomatizations of Two Types of Shapley Values for Games on Union Closed Systems
van den Brink, René; Katsev, Ilya V.; van der Laan, Gerard - 2009
A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the...
Persistent link: https://www.econbiz.de/10014046375
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The Socially Stable Core in Structured Transferable Utility Games
Herings, P. Jean-Jacques; van der Laan, Gerard; Talman, Dolf - 2004
of players. The social structure is utilized to refine the core of the game. For every coalition the relative strength of … stable core is the set of socially stable elements of the core. We show that the socially stable core is non-empty if the … game itself is socially stable. In general the socially stable core consists of a finite number of faces of the core and …
Persistent link: https://www.econbiz.de/10010325448