scholarly journals Parallel characterizations of a generalized Shapley value and a generalized Banzhaf value for cooperative games with level structure of cooperation

2011 ◽  
Vol 52 (1) ◽  
pp. 21-27 ◽  
Author(s):  
M. Álvarez-Mozos ◽  
O. Tejada
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Level Structure ◽  
Banzhaf Value

Shapley-Based Analysis of the Leadership Formation in Social Networks

2019 ◽  
pp. 357-390
Author(s):  
Ivan Belik
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Real Life ◽  
Importance Measure ◽  
Theory Theory ◽  
Leadership Position ◽  
Leadership Formation ◽  
Game Theoretic ◽  
As Graph ◽  
Research Domains

The dynamic nature of networks formation requires the development of multidisciplinary methods for the effective social network analysis. The research presented in this chapter is motivated by the necessity to overcome the limitation of using analytical methods from the originally disconnected research domains. Hence, the authors present an approach based on techniques from different areas, such as graph theory, theory of algorithms, and game theory. Specifically, this chapter is based on the analysis of how an agent can move towards leadership in real-life socioeconomic networks. For the agent's importance measure, the authors employed a Shapley value concept from the area of cooperative games. Shapley value is interpreted as the node centrality that corresponds to the significance of the agent within a socioeconomic network. Employing game theoretic concept, the authors introduced an algorithmic approach that detects the potential connectivity modifications required to increase an agent's leadership position.

THE SHAPLEY VALUE, THE OWEN VALUE, AND THE VEIL OF IGNORANCE

2009 ◽  
Vol 11 (04) ◽  
pp. 453-457 ◽  
Author(s):  
ANDRÉ CASAJUS
Keyword(s):  
Shapley Value ◽  
Banzhaf Value ◽  
Owen Value ◽  
Symmetric Distributions ◽  
Veil Of Ignorance ◽  
Tu Games ◽  
The Shapley Value ◽  
The Veil ◽  
Cooperation Structure

We show that the Owen value for TU games with a cooperation structure extends the Shapley value in a consistent way. In particular, the Shapley value is the expected Owen value for all symmetric distributions on the partitions of the player set. Similar extensions of the Banzhaf value do not show this property.

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).

Axiomatizations of the normalized Banzhaf value and the Shapley value

1998 ◽  
Vol 15 (4) ◽  
pp. 567-582 ◽  
Author(s):  
René van den Brink ◽  
Gerard van der Laan
Keyword(s):  
Shapley Value ◽  
Banzhaf Value ◽  
The Shapley Value

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.

scholarly journals Some Recursive Definitions for Linear Values of Cooperative TU Games

Game Theory ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Irinel Dragan
Keyword(s):  
Shapley Value ◽  
Banzhaf Value ◽  
Tu Games ◽  
The Shapley Value ◽  
Cooperative Tu Games ◽  
Power Game ◽  
Recursive Definitions

We give recursive definitions for the Banzhaf Value and the Semivalues of cooperative TU games. These definitions were suggested by the concept of potential for the Shapley Value due to Hart and Mas-Colell and by some results of the author who introduced the potentials of these values and the Power Game of a given game.

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