Open AccessJournal Article
Airport interval games and their Shapley value
TLDR
In this paper, the authors dealt with the research area of cooperative interval games arising from airport situations with interval data, and presented and identified the interval Baker-Thompson rule, which is the most common rule in interval games.Abstract:
This paper deals with the research area of cooperative interval games arising from airport situations with interval data. The major topic of the paper is to present and identify the interval Baker–Thompson rule.read more
Citations
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Journal ArticleDOI
Cooperative interval games: a survey
Rodica Branzei,Oana Branzei,S. Zeynep Alparslan Gök,S. Zeynep Alparslan Gök,Stef Tijs,Stef Tijs +5 more
TL;DR: The state-of-the-art in this young field of research is presented, how the model of cooperative interval games extends the cooperative game theory literature is discussed, and its existing and potential applications in economic and operations research situations with interval data are reviewed.
Journal ArticleDOI
The interval Shapley value: an axiomatization
TL;DR: The interval Shapley value is characterized with the aid of the properties of additivity, efficiency, symmetry and dummy player, which are straightforward generalizations of the corresponding properties in the classical cooperative game theory.
Journal ArticleDOI
How to handle interval solutions for cooperative interval games
TL;DR: The research question addressed here is: How to determine for each player his/her/its payoff generated by cooperation within the grand coalition – in the promised range of payoffs to establish such cooperation – after the uncertainty on the payoff for thegrand coalition is resolved.
Book ChapterDOI
Dynamical Gene-Environment Networks Under Ellipsoidal Uncertainty: Set-Theoretic Regression Analysis Based on Ellipsoidal OR
TL;DR: In this article, the authors consider dynamical gene-environment networks under ellipsoidal uncertainty and discuss the corresponding set-theoretic regression models, in particular in view of their solvability by interior point methods and semidefinite programming.
Journal ArticleDOI
Cost Sharing under Uncertainty: An Algorithmic Approach to Cooperative Interval-Valued Games
Alf Kimms,Julia Drechsel +1 more
TL;DR: In this paper, a general mathematical programming algorithm is presented to find an element in the interval core of a cooperative interval-valued game, which can be applied to find a solution to the problem of lot sizing with uncertain demand.
References
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Book ChapterDOI
A Value for n-person Games
TL;DR: In this paper, an examination of elementary properties of a value for the essential case is presented, which is deduced from a set of three axioms, having simple intuitive interpretations.
Journal ArticleDOI
A Simple Expression for the Shapley Value in a Special Case
S. C. Littlechild,Guillermo Owen +1 more
TL;DR: In this article, the authors present a simple and easily calculated expression for the Shapley value whenever the characteristic function is a "cost" function with the property that the cost of any subset of players is equal to the "largest" player in that subset.
BookDOI
Cooperative Games, Solutions and Applications
TL;DR: In this article, a game theoretic approach to the cost allocation problem by means of the?-value, the Nucleolus and the Shapley value is presented. But this approach is limited to the case of cooperative games.
Journal ArticleDOI
Aircraft Landing Fees: A Game Theory Approach
S. C. Littlechild,G. F. Thompson +1 more
TL;DR: In this article, the authors explore the implications of an alternative pricing philosophy where the common costs of runway construction are shared among the different aircraft types according to a club principle, and suggest new rules of thumb for allocating common costs based on the Shapley value and the nucleolus.
Journal ArticleDOI
Cooperation under interval uncertainty
TL;DR: In this article, the classical theory of two-person cooperative games is extended to two-player cooperative games with interval uncertainty, and the core, balancedness, superadditivity and related topics are studied.