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On the 1-Nucleolus for classes of cooperative games
Estévez-Fernández, A.; Borm, P.; Fiestras-Janeiro, M.G.; … - 2015
This paper analyzes the 1-nucleolus and, in particular, its relation to the nucleolus and compromise value. It is seen that the 1-nucleolus of a cooperative game can be characterized using a combination of standard bankruptcy rules for associated bankruptcy problems. In particular, for any...
Persistent link: https://www.econbiz.de/10011376297
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Computation of the nucleolus for a class of disjunctive games with a permission structure
Brink, René van den; Katsev, Ilya; Laan, Gerard van der - 2008
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/10011376532
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An algorithm for computing the nucleolus of disjunctive additive games with an acyclic permission structure
Brink, René van den; Katsev, Ilya; Laan, Gerard van der - 2008
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/10011377258
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The restricted core for totally positive games with ordered players
Brink, René van den; Laan, Gerard van der; Vasilʹev, … - 2009
nonnegative), and there is some hierarchical ordering of the players. In this paper we introduce the 'Restricted Core' for such … of the players. For totally positive games this solution is always contained in the 'Core', and contains the well … coalitions). For special orderings it equals the Core, respectively Shapley value. We provide an axiomatization and apply this …
Persistent link: https://www.econbiz.de/10011378242
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The Harsanyi set for cooperative TU-games
Vasilʹev, Valerij A.; Laan, Gerard van der - 2001
Harsanyi set is related to the Core and Weberset. We also characterize the Harsanyi mapping as the unique mappingsatisfying a …
Persistent link: https://www.econbiz.de/10011313932
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On Harsanyi payoff vectors and the Weber set
Derks, Jean J. M.; Laan, Gerard van der; Vasilʹev, … - 2002
, these results state already that the set of Harsanyi payoff vectors is given by the core of an associated convex game, a …
Persistent link: https://www.econbiz.de/10011327842
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Interval solutions for Tu-games
Brink, Rene (J.R.) van den; Palanci, Osman; … - 2017
Standard solutions for TU-games assign to every TU-game a payoff vector. However, if there is uncertainty about the payoff allocation then we cannot just assign a specific payoff to every player. Therefore, in this paper we introduce interval solutions for TU-games which assign to every TU-game...
Persistent link: https://www.econbiz.de/10011735157
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Sign properties and axiomatizations of the weighted division value
Li, Whenzong; Xu, Genjiu; Brink, René van den - 2021
In this paper, we study axiomatic foundations of the class of weighted division values. Firstly, while keeping efficiency, additivity and the nullifying player property from the original axiomatization of the equal division value, we consider relaxations of symmetry in line with Casajus (2019)...
Persistent link: https://www.econbiz.de/10012795320
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From hierarchies to levels : new solutions for games
Álvarez-Mozos, Mikel; Brink, René van den; Laan, … - 2015
Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict players ́possibilities to cooperate. In this paper, we...
Persistent link: https://www.econbiz.de/10010532576
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Efficiency and collusion neutrality of solutions for cooperative TU-games
Brink, René van den - 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/10011378796