Cooperative Game Theory and Applications

Curiel, Imma

doi:10.1007/978-1-4757-4871-0

Cited by 150 publications

(43 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Classical results show under which conditions the core is nonempty, and give the structure of the core when the game is convex. A related notion is the Weber set (see, e.g., [3]), which is proven to always contain the core, with equality attained in case of convexity.…”

Section: Introductionmentioning

confidence: 99%

A new approach to the core and Weber set of multichoice games

Grabisch

Xie

2007

Math Meth Oper Res

View full text Add to dashboard Cite

To cite this version:Michel Grabisch, Lijue Xie. A new approach to the core and Weber set of multichoice games. Mathematical Methods of Operations Research, Springer Verlag, 2007, 66 (3) 1 Abstract Multichoice games have been introduced by Hsiao and Raghavan as a generalization of classical cooperative games. An importantnotion in cooperative game theory is the core of the game, as it contains the rational imputations for players. We propose two definitions for the core of a multichoice game, the first one is called the precore and is a direct generalization of the classical definition. We show that the precore coincides with the definition proposed by Faigle, and that the set of imputations may be unbounded, which makes its application questionable. A second definition is proposed, imposing normalization at each level, causing the core to be a convex compact set. We study its properties, introducing balancedness and marginal worth vectors, and defining the Weber set and the pre-Weber set. We show that the classical properties of inclusion of the (pre)core into the (pre)-Weber set as well as their coincidence in the convex case remain valid. A last section makes a comparison with the core defined by van den Nouweland et al.

show abstract

Section: Introductionmentioning

confidence: 99%

A new approach to the core and Weber set of multichoice games

Grabisch

Xie

2007

Math Meth Oper Res

View full text Add to dashboard Cite

show abstract

“…It can be shown, however, that the nucleolus and prenucleolus coincide for TU games with non-empty core 3 and for superadditive TU games. 4 An equivalent way of defining the two solution concepts is in terms of objections and counterobjections. We define these as follows.…”

Section: Definition 22 the Prenucleolus Of A Gamementioning

confidence: 99%

On the coincidence of the prenucleolus and the Shapley value

Kar¹,

Mitra²,

Mutuswami³

2009

Mathematical Social Sciences

View full text Add to dashboard Cite

show abstract

“…The above definition is the central concept of cooperative game theory (see, e.g., [14,11,3,44]). The only difference between games and capacities is that monotonicity is dropped for the former.…”

Section: Capacities Fuzzy Measures Games and The Likementioning

confidence: 99%

Capacities and Games on Lattices: A Survey of Results

Grabisch

2005

Modeling Decisions for Artificial Intelligence

View full text Add to dashboard Cite

We provide a survey of recent developments about capacities (or fuzzy measures) and ccoperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of usual tools in these theories, such as the Choquet integral, the Möbius transform, and the Shapley value.

show abstract

Cooperative Game Theory and Applications

Cited by 150 publications

References 62 publications

A new approach to the core and Weber set of multichoice games

A new approach to the core and Weber set of multichoice games

On the coincidence of the prenucleolus and the Shapley value

Capacities and Games on Lattices: A Survey of Results

Contact Info

Product

Resources

About