scholarly journals Axiomatizations of the Shapley value for cooperative games on antimatroids

2003 ◽  
Vol 57 (1) ◽  
pp. 49-65 ◽  
Author(s):  
E. Algaba ◽  
J. M. Bilbao ◽  
R. van den Brink ◽  
A. Jim�nez-Losada
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
The Shapley Value

The Shapley value of cooperative games under fuzzy settings: a survey

2013 ◽  
Vol 43 (1) ◽  
pp. 75-95 ◽  
Author(s):  
Surajit Borkotokey ◽  
Radko Mesiar
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
The Shapley Value

AN AXIOM SYSTEM FOR A VALUE FOR GAMES IN PARTITION FUNCTION FORM

2005 ◽  
Vol 07 (01) ◽  
pp. 63-72 ◽  
Author(s):  
M. J. ALBIZURI ◽  
J. ARIN ◽  
J. RUBIO
Keyword(s):  
Partition Function ◽  
Shapley Value ◽  
Cooperative Games ◽  
Axiom System ◽  
Axiomatic Characterization ◽  
Transferable Utility ◽  
Function Form ◽  
A Value ◽  
The Shapley Value ◽  
Partition Function Form

Lucas and Trall (1963) defined the games in partition function form as a generalization of the cooperative games with transferable utility. In our work we propose by means of an axiomatic characterization a solution for such games in partition function form. This solution will be a generalization of the Shapley value (1953).

scholarly journals Hart–Mas-Colell consistency and the core in convex games

2021 ◽  
Author(s):  
Bas Dietzenbacher ◽  
Peter Sudhölter
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Individual Rationality ◽  
Transferable Utility ◽  
Convex Games ◽  
The Core ◽  
The Shapley Value ◽  
Scale Covariance

AbstractThis paper formally introduces Hart–Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covariance, superadditivity, weak Hart–Mas-Colell consistency, and converse Hart–Mas-Colell consistency. This family consists of (a) the Shapley value, (b) all homothetic images of the core with the Shapley value as center of homothety and with positive ratios of homothety not larger than one, and (c) their relative interiors.

Irrational-Behavior-Proof Conditions Based on Limit Characteristic Functions

2019 ◽  
Vol 7 (1) ◽  
pp. 1-16
Author(s):  
Cui Liu ◽  
Hongwei Gao ◽  
Ovanes Petrosian ◽  
Juan Xue ◽  
Lei Wang
Keyword(s):  
Characteristic Function ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Games ◽  
Characteristic Functions ◽  
The Core ◽  
The Shapley Value ◽  
Irrational Behavior ◽  
The Individual

Abstract Irrational-behavior-proof (IBP) conditions are important aspects to keep stable cooperation in dynamic cooperative games. In this paper, we focus on the establishment of IBP conditions. Firstly, the relations of three kinds of IBP conditions are described. An example is given to show that they may not hold, which could lead to the fail of cooperation. Then, based on a kind of limit characteristic function, all these conditions are proved to be true along the cooperative trajectory in a transformed cooperative game. It is surprising that these facts depend only upon the individual rationalities of players for the Shapley value and the group rationalities of players for the core. Finally, an illustrative example is given.

scholarly journals Algorithms for computing the Shapley value of cooperative games on lattices

2018 ◽  
Vol 249 ◽  
pp. 91-105
Author(s):  
Khaled Maafa ◽  
Lhouari Nourine ◽  
Mohammed Said Radjef
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
The Shapley Value

scholarly journals Collinearity between the Shapley value and the egalitarian division rules for cooperative games

OR Spectrum ◽  
1996 ◽  
Vol 18 (2) ◽  
pp. 97-105 ◽  
Author(s):  
Irinel Dragan ◽  
Theo Driessen ◽  
Yukihiko Funaki
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
The Shapley Value
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