An Axiomatization of the Interval Shapley Value and on Some Interval Solution Concepts

Date

2014-06-27

Author

PALANCI, Osman
ALPARSLAN GÖK, Sırma Zeynep
Weber, Gerhard Wilhelm

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

130
views

0
downloads

The Shapley value, one of the most common solution concepts in Operations Research applications of cooperative game theory, is defined and axiomatically characterized in different game-theoretical models. In this paper, we focus on the Shapley value for cooperative games where the set of players is finite and the coalition values are compact intervals of real numbers. In this study, we study the properties of the interval Shapley value on the class of size monotonic interval games, and axiomatically characterize its restriction to a special subclass of cooperative interval games by using fairness property, efficiency and the null player property. Further, we introduce the interval Banzhaf value and the interval egalitarian rule. Finally, the paper ends with a conclusion and an outlook to future studies.

Subject Keywords

Shapley value, Banzhaf value, Egalitarian rule, Interval uncertainty, Fairness property

URI

https://hdl.handle.net/11511/53310

Collections

Graduate School of Applied Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

The interval Shapley value: an axiomatization Gok, S. Z. Alparslan; Branzei, R.; Tijs, S. (Springer Science and Business Media LLC, 2010-06-01) The Shapley value, one of the most widespread concepts in operations Research applications of cooperative game theory, was defined and axiomatically characterized in different game-theoretic models. Recently much research work has been done in order to extend OR models and methods, in particular cooperative game theory, for situations with interval data. This paper focuses on the Shapley value for cooperative games where the set of players is finite and the coalition values are compact intervals of real num...
Cooperative grey games and the grey Shapley value PALANCI, Osman; PALANCI, Osman; Ergun, S.; Weber, Gerhard Wilhelm (2015-08-03) This contribution is located in the common area of operational research and economics, with a close relation and joint future potential with optimization: game theory. We focus on collaborative game theory under uncertainty. This study is on a new class of cooperative games where the set of players is finite and the coalition values are interval grey numbers. An interesting solution concept, the grey Shapley value, is introduced and characterized with the properties of additivity, efficiency, symmetry and d...
An Approach for determining process economy parameters of multivariate loss functions Özkan, Gökçe; Köksal, Gülser; Department of Industrial Engineering (2016) The aim of this study is to provide an effective method for determining parameters of multivariate loss functions, which are related with process economics. The loss functions are widely used in product and process design and other quality engineering applications. Although there are several studies about different types of loss functions, there is a lack of studies on determining cost matrix parameters of these functions. For this purpose, we propose a method based on multi-objective decision making tools....
Cooperation under interval uncertainty Alparslan-Goek, S. Zeynep; Miquel, Silvia; Tijs, Stef H. (2009-03-01) In this paper, the classical theory of two-person cooperative games is extended to two-person cooperative games with interval uncertainty. The core, balancedness, superadditivity and related topics are studied. Solutions called psi(alpha)-values are introduced and characterizations are given.
An improved method for inference of piecewise linear systems by detecting jumps using derivative estimation Selcuk, A. M.; Öktem, Hüseyin Avni (Elsevier BV, 2009-08-01) Inference of dynamical systems using piecewise linear models is a promising active research area. Most of the investigations in this field have been stimulated by the research in functional genomics. In this article we study the inference problem in piecewise linear systems. We propose first identifying the state transitions by detecting the jumps of the derivative estimates, then finding the guard conditions of the state transitions (thresholds) from the values of the state variables at the state transitio...

Citation Formats

O. PALANCI, S. Z. ALPARSLAN GÖK, and G. W. Weber, “An Axiomatization of the Interval Shapley Value and on Some Interval Solution Concepts,” 2014, vol. 8, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/53310.