scholarly journals Multiobjective Games for Detecting Abnormally Expressed Genes

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 350 ◽  
Author(s):  
Vito Fragnelli ◽  
Lucia Pusillo
Keyword(s):  
Shapley Value ◽  
Axiomatic Characterization ◽  
Banzhaf Value ◽  
Multicriteria Game

A class of multiobjective games with applications to a medicine setting is studied. We consider the vector Shapley value and the vector Banzhaf value for a multicriteria game and we apply them to a microarray game. We give an axiomatic characterization too.

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 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.

The modified Banzhaf value for games with coalition structure: an axiomatic characterization

2002 ◽  
Vol 43 (1) ◽  
pp. 45-54 ◽  
Author(s):  
Rafael Amer ◽  
Francese Carreras ◽  
José Miguel Giménez
Keyword(s):  
Coalition Structure ◽  
Axiomatic Characterization ◽  
Banzhaf Value

VALUES FOR GAMES ON THE CYCLES OF A DIGRAPH

2012 ◽  
Vol 14 (02) ◽  
pp. 1250008
Author(s):  
WILLIAM OLVERA-LOPEZ ◽  
FRANCISCO SANCHEZ-SANCHEZ
Keyword(s):  
Mathematical Model ◽  
Characteristic Function ◽  
Shapley Value ◽  
Cooperative Games ◽  
Axiomatic Characterization ◽  
Efficient Solutions ◽  
Function Form ◽  
New Class ◽  
Characteristic Function Form

In this paper we introduce a new class of cooperative games. We define a characteristic function over the cycles of a digraph. We present a mathematical model for this situation and an axiomatic characterization of a solution for this class of cooperative games. This is introduced as a method to measure the importance of the nodes in a digraph, and can be related with the Shapley value of a game in characteristic function form. Also, we extend the modeling by applying coalitional structures for the nodes and r-efficient solutions, where the allocation amount is a real number r, showing axiomatic solutions in both cases.

scholarly journals LS-Tree: Model Interpretation When the Data Are Linguistic

2020 ◽  
Vol 34 (04) ◽  
pp. 3454-3461
Author(s):  
Jianbo Chen ◽  
Michael Jordan
Keyword(s):  
Game Theory ◽  
Axiomatic Characterization ◽  
Language Models ◽  
Banzhaf Value ◽  
Data Sets ◽  
Coalitional Game ◽  
Classification Models ◽  
Tree Model ◽  
Model Interpretation

We study the problem of interpreting trained classification models in the setting of linguistic data sets. Leveraging a parse tree, we propose to assign least-squares-based importance scores to each word of an instance by exploiting syntactic constituency structure. We establish an axiomatic characterization of these importance scores by relating them to the Banzhaf value in coalitional game theory. Based on these importance scores, we develop a principled method for detecting and quantifying interactions between words in a sentence. We demonstrate that the proposed method can aid in interpretability and diagnostics for several widely-used language models.

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