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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

The locally partial permission value for games with a permission structure

Wu, Hao; Brink, René van den; Estévez-Fernández, Arantza - 2022

Cooperative games with a permission structure are useful tools for analyzing the impact of hierarchical structures on allocation problems in Economics and Operations Research. In this paper, we propose a generalization of the local disjunctive and the local conjunctive permission approaches...

Persistent link: https://www.econbiz.de/10013207269

Distributing dividends in games with ordered players

Brink, René van den; Laan, Gerard van der; Vasilʹev, … - 2006

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 solution for TU-games assigns a set of payoff vectors to every TU-game. Some solutions that are based on distributing...

Persistent link: https://www.econbiz.de/10011350374

Players indifferent to cooperate and characterizations of the Shapley value

Manuel, Conrado; Gonzalez-Aranguena, Enrique; Brink, … - 2012

Persistent link: https://www.econbiz.de/10009722669

Axiomatizations of two types of shapley values for games on union closed systems

Brink, René van den; Katsev, Ilya; Laan, Gerard van der - 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/10011378792

From hierarchies to levels : new solutions for games with hierarchical structure

Álvarez-Mozos, Mikel; Brink, René van den; Laan, … - 2015

Persistent link: https://www.econbiz.de/10011280073

Harsanyi power solutions for games on union stable systems

Algaba, Encarnacion; Bilbao, Jesús Mario; Brink, René … - 2011

Persistent link: https://www.econbiz.de/10009720696

Power measures and solutions for games under precedence constraints

Algaba, Encarnacion; Brink, René van den; Dietz, Chris - 2015

the player set that is represented by a digraph. We consider games under precedence constraints introduced by Faigle and … coalition. The hierarchical strength of a player in a coalition in an acyclic digraph is the number of admissible permutations … (those in which successors in the digraph enter before predecessors) where this player is the last of that coalition to enter …

Persistent link: https://www.econbiz.de/10010464783

Harsanyi power solutions for graph-restricted games

Brink, René van den; Laan, Gerard van der; Pruzhansky, … - 2004

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 solution for TU-games assigns a set of payoff distributions (possibly empty or consisting of a unique element) to every...

Persistent link: https://www.econbiz.de/10011338005

The restricted core for totally positive games with ordered players

Brink, René van den; Laan, Gerard van der; Vasilʹev, … - 2009

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