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 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.

scholarly journals Allocation Problems, by the Method of Alternative Representation of the Inverse Set, for Values of Cooperative TU Games

2021 ◽  
Vol 6 (3) ◽  
pp. 173-177
Author(s):  
Irinel Dragan
Keyword(s):  
Shapley Value ◽  
Rational Solution ◽  
Tu Games ◽  
Alternative Representation ◽  
The Core ◽  
The Shapley Value ◽  
Cooperative Tu Games ◽  
The Family ◽  
Unique Parameter ◽  
Definition Of

In earlier works, we introduced the Inverse Problem, relative to the Shapley Value, as follows: for a given n-dimensional vector L, find out the transferable utilities’ games , such that  The same problem has been discussed further for Semivalues. A connected problem has been considered more recently: find out TU-games for which the Shapley Value equals L, and this value is coalitional rational, that is belongs to the Core of the game . Then, the same problem was discussed for other two linear values: the Egalitarian Allocation and the Egalitarian Nonseparable Contribution, even though these are not Semivalues. To solve such problems, we tried to find a solution in the family of so called Almost Null Games of the Inverse Set, relative to the Shapley Value, by imposing to games in the family, the coalitional rationality conditions. In the present paper, we use the same idea, but a new tool, an Alternative Representation of Semivalues. To get such a representation, the definition of the Binomial Semivalues due to A. Puente was extended to all Semivalues. Then, we looked for a coalitional rational solution in the Family of Almost Null games of the Inverse Set, relative to the Shapley Value. In each case, such games depend on a unique parameter, so that the coalitional rationality will be expressed by a simple inequality, determined by a number, the coalitional rationality threshold. The relationships between the three numbers corresponding to the above three efficient values have been found. Some numerical examples of the method are given.

scholarly journals ON THE SEMIVALUES AND THE POWER CORE OF COOPERATIVE TU GAMES

2001 ◽  
Vol 03 (02n03) ◽  
pp. 127-139 ◽  
Author(s):  
IRINEL DRAGAN ◽  
JUAN ENRIQUE MARTINEZ-LEGAZ
Keyword(s):  
Shapley Value ◽  
Direct Proof ◽  
Weighted Average ◽  
Potential Game ◽  
Tu Games ◽  
A Value ◽  
The Shapley Value ◽  
Cooperative Tu Games ◽  
System Of Inequalities ◽  
Per Capita

A weighted average worth per capita formula is presented for any semivalue of a TU game. Further, this formula is used to derive a characterisation of the class of games with the property that a given semivalue belongs to the power core of the game, by means of a linear system of inequalities. It is shown that for the Shapley value, the only efficient semivalue, this system reduces to the system already obtained by Inarra and Usategui. The potential approach is also used even for the more general case of values possessing a potential. A direct proof shows that for a value possessing a potential, the value of a game is in the power core relative to this value, if and only if the potential game is weak average convex. From this result, it follows that for a game and each of its subgames the value possessing a potential is in the corresponding power cores, if and only if the potential game relative to the value is average convex. This is an extension of the result obtained by Marin–Solano and Rafels for the Shapley value, proved by using the dividend form of the game.

On a family of values for TU-games generalizing the Shapley value

2013 ◽  
Vol 65 (2) ◽  
pp. 105-111 ◽  
Author(s):  
Tadeusz Radzik ◽  
Theo Driessen
Keyword(s):  
Shapley Value ◽  
Tu Games ◽  
The Shapley Value

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 THE SHAPLEY VALUE FOR PARTITION FUNCTION FORM GAMES

2007 ◽  
Vol 09 (02) ◽  
pp. 353-360 ◽  
Author(s):  
KIM HANG PHAM DO ◽  
HENK NORDE
Keyword(s):  
Partition Function ◽  
Shapley Value ◽  
Function Form ◽  
Tu Games ◽  
The Shapley Value ◽  
Partition Function Form Games ◽  
Partition Function Form

Different axiomatizations of the Shapley value for TU games can be found in the literature. The Shapley value has been generalized in several ways to the class of games in partition function form. In this paper we discuss another generalization of the Shapley value and provide a characterization.

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