The Equivalence of the Minimal Dominant Set and the Myopic Stable Set for Coalition Function Form Games PDF Download
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Author: Peter Jean-Jacques Herings
Publisher:
ISBN:
Category :
Languages : en
Pages :
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In cooperative games, the coalition structure core is, despite its potential emptiness, one of the most popular solutions. While it is a fundamentally static concept, the consideration of a sequential extension of the underlying dominance correspondence gave rise to a selection of non-empty generalizations. Among these, the payoff-equivalence minimal dominant set and the myopic stable set are defined by a similar set of conditions. We identify some problems with the payoff-equivalence minimal dominant set and propose an appropriate reformulation called the minimal dominant set. We show that replacing asymptotic external stability by sequential weak dominance leaves the myopic stable set unaffected. The myopic stable set is therefore equivalent to the minimal dominant set.
Author: Peter Jean-Jacques Herings
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
In cooperative games, the coalition structure core is, despite its potential emptiness, one of the most popular solutions. While it is a fundamentally static concept, the consideration of a sequential extension of the underlying dominance correspondence gave rise to a selection of non-empty generalizations. Among these, the payoff-equivalence minimal dominant set and the myopic stable set are defined by a similar set of conditions. We identify some problems with the payoff-equivalence minimal dominant set and propose an appropriate reformulation called the minimal dominant set. We show that replacing asymptotic external stability by sequential weak dominance leaves the myopic stable set unaffected. The myopic stable set is therefore equivalent to the minimal dominant set.
Author: László Á Kóczy
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
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A set of outcomes for a TU-game in characteristic function form is dominant if it is, with respect to an outsider-independent dominance relation, accessible (or admissible) and closed. This outsider-independent dominance relation is restrictive in the sense that a deviating coalition cannot determine the payoffs of those coalitions that are not involved in the deviation. The minimal (for inclusion) dominant set is non-empty and for a game with a non-empty coalition structure core, the minimal dominant set returns this core.
Author: László Á Kóczy
Publisher:
ISBN: 9789639588226
Category : Environmental economics
Languages : en
Pages : 21
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Author: Robert Wernick Rosenthal
Publisher:
ISBN:
Category : Game theory
Languages : en
Pages : 132
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Author: Shigeo Muto
Publisher:
ISBN:
Category : Game theory
Languages : en
Pages : 306
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Stable sets and subsolutions are studied mainly for symmetric, n-person, characteristic-function form games (n;k) in which k-person coalitions are strongly vital, i.e., v(s)
Author: Kai Michaelis
Publisher:
ISBN:
Category : Game theory
Languages : en
Pages : 126
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Author: Massimo Morelli
Publisher:
ISBN:
Category : Game theory
Languages : en
Pages : 26
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Author: Gleb A. Koshevoy
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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We introduce a theory on marginal values and their core stability for cooperative games with arbitrary coalition structure. The theory is based on the notion of nested sets and the complex of nested sets associated to an arbitrary set system and the M-extension of a game for this set. For a set system being a building set or partition system, the corresponding complex is a polyhedral complex, and the vertices of this complex correspond to maximal strictly nested sets. To each maximal strictly nested set is associated a rooted tree. Given characteristic function, to every maximal strictly nested set a marginal value is associated to a corresponding rooted tree as in [9]. We show that the same marginal value is obtained by using the M-extension for every permutation that is associated to the rooted tree. The GC-solution is de ned as the average of the marginal values over all maximal strictly nested sets. The solution can be viewed as the gravity center of the image of the vertices of the polyhedral complex. The GC-solution di ers from the Myerson-kind value de ned in [2] for union stable structures. The HS-solution is defined as the average of marginal values over the subclass of so-called half-space nested sets. The NT-solution is another solution and is defined as the average of marginal values over the subclass of NT-nested sets. For graphical buildings the collection of NT-nested sets corresponds to the set of spanning normal trees on the underlying graph and the NT-solution coincides with the average tree solution. We also study core stability of the solutions and show that both the HS-solution and NT-solution belong to the core under half-space supermodularity, which is a weaker condition than convexity of the game. For an arbitrary set system we show that there exists a unique minimal building set containing the set system. As solutions we take the solutions for this building covering by extending in a natural way the characteristic function to it by using its Mobius inversion.
Author: Andrew John Sterge
Publisher:
ISBN:
Category : Coalitions
Languages : en
Pages : 636
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Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 786
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