8 found
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  1.  17
    Consistency, Population Solidarity, and Egalitarian Solutions for TU-Games.René van den Brink, Youngsub Chun, Yukihiko Funaki & Boram Park - 2016 - Theory and Decision 81 (3):427-447.
    A solution for cooperative games with transferable utility, or simply TU-games, assigns a payoff vector to every TU-game. In this paper we discuss two classes of equal surplus sharing solutions. The first class consists of all convex combinations of the equal division solution and the center-of-gravity of the imputation-set value. The second class is the dual class consisting of all convex combinations of the equal division solution and the egalitarian non-separable contribution value. We provide characterizations of the two classes of (...)
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  2.  59
    Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games.René van den Brink & Yukihiko Funaki - 2009 - Theory and Decision 67 (3):303-340.
    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 (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of solutions on variable and fixed (...)
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  3. Characterizations of the Β- and the Degree Network Power Measure.René Van Den Brink, Peter Borm, Ruud Hendrickx & Guillermo Owen - 2008 - Theory and Decision 64 (4):519-536.
    A symmetric network consists of a set of positions and a set of bilateral links between these positions. For every symmetric network we define a cooperative transferable utility game that measures the “power” of each coalition of positions in the network. Applying the Shapley value to this game yields a network power measure, the β-measure, which reflects the power of the individual positions in the network. Applying this power distribution method iteratively yields a limit distribution, which turns out to be (...)
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  4.  92
    Digraph Competitions and Cooperative Games.René van Den Brink & Peter Borm - 2002 - Theory and Decision 53 (4):327-342.
    Digraph games are cooperative TU-games associated to domination structures which can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles in social choice theory. The Shapley value, core, marginal vectors and selectope vectors of digraph games are characterized in terms of so-called simple score vectors. A general characterization of the class of (almost positive) TU-games where each selectope vector is a marginal vector is provided in terms of game semi-circuits. (...)
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  5.  96
    Games with a Local Permission Structure: Separation of Authority and Value Generation. [REVIEW]René van den Brink & Chris Dietz - 2014 - Theory and Decision 76 (3):343-361.
    It is known that peer group games are a special class of games with a permission structure. However, peer group games are also a special class of digraph games. To be specific, they are digraph games in which the digraph is the transitive closure of a rooted tree. In this paper we first argue that some known results on solutions for peer group games hold more general for digraph games. Second, we generalize both digraph games as well as games with (...)
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  6.  53
    A Banzhaf Share Function for Cooperative Games in Coalition Structure.Gerard van Der Laan & René van Den Brink - 2002 - Theory and Decision 53 (1):61-86.
    A cooperative game with transferable utility–or simply a TU-game– describes a situation in which players can obtain certain payoffs by cooperation. A value function for these games assigns to every TU-game a distribution of payoffs over the players. Well-known solutions for TU-games are the Shapley and the Banzhaf value. An alternative type of solution is the concept of share function, which assigns to every player in a TU-game its share in the worth of the grand coalition. In this paper we (...)
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  7.  70
    Internal Slackening Scoring Methods.Marco Slikker, Peter Borm & René van den Brink - 2012 - Theory and Decision 72 (4):445-462.
    We deal with the ranking problem of the nodes in a directed graph. The bilateral relationships specified by a directed graph may reflect the outcomes of a sport competition, the mutual reference structure between websites, or a group preference structure over alternatives. We introduce a class of scoring methods for directed graphs, indexed by a single nonnegative parameter α. This parameter reflects the internal slackening of a node within an underlying iterative process. The class of so-called internal slackening scoring methods, (...)
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  8.  37
    Axiomatization of a Class of Share Functions for N-Person Games.Gerard van Der Laan & René van Den Brink - 1998 - Theory and Decision 44 (2):117-148.
    The Shapley value is the unique value defined on the class of cooperative games in characteristic function form which satisfies certain intuitively reasonable axioms. Alternatively, the Banzhaf value is the unique value satisfying a different set of axioms. The main drawback of the latter value is that it does not satisfy the efficiency axiom, so that the sum of the values assigned to the players does not need to be equal to the worth of the grand coalition. By definition, the (...)
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