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Conditions for the uniqueness of the Gately point for cooperative games

  • We are studying the Gately point, an established solution concept for cooperative games. We point out that there are superadditive games for which the Gately point is not unique, i.e. in general the concept is rather set-valued than an actual point. We derive conditions under which the Gately point is guaranteed to be a unique imputation and provide a geometric interpretation. The Gately point can be understood as the intersection of a line defined by two points with the set of imputations. Our uniqueness conditions guarantee that these two points do not coincide. We provide demonstrative interpretations for negative propensities to disrupt. We briefly show that our uniqueness conditions for the Gately point include quasibalanced games and discuss the relation of the Gately point to the τ-value in this context. Finally, we point out relations to cost games and the ACA method and end upon a few remarks on the implementation of the Gately point and an upcoming software package for cooperative game theory.

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Metadaten
Author:Jochen StaudacherORCiDGND, Johannes Anwander
URL / DOI:https://arxiv.org/pdf/1901.01485.pdf
Document Type:Preprint
Language:English
Date of Publication (online):2019/01/08
Year of first Publication:2019
Tag:cooperative game theory
GND Keyword:Spieltheorie
Number of pages:10
Institutes:Fakultät Informatik
IFI - Institut für Internationalisierung
Dewey Decimal Classification:3 Sozialwissenschaften / 32 Politikwissenschaft
3 Sozialwissenschaften / 33 Wirtschaft
5 Naturwissenschaften und Mathematik / 51 Mathematik
Research focus:FSP4: Soziale Innovationen
Publication Lists:Staudacher, Jochen
Publication reviewed:nicht begutachtet
Licence (German):Es gilt das deutsche Urheberrecht
Release Date:2021/02/16
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