scholarly journals The Shapley Value for Partition Function Form Games

2002 ◽  
Author(s):  
Kim Hang Pham Do ◽  
Henk W. Norde
Keyword(s):  
Partition Function ◽  
Shapley Value ◽  
Function Form ◽  
The Shapley Value ◽  
Partition Function Form Games ◽  
Partition Function Form

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.

scholarly journals Marginality and convexity in partition function form games

2021 ◽  
Author(s):  
J. M. Alonso-Meijide ◽  
M. Álvarez-Mozos ◽  
M. G. Fiestras-Janeiro ◽  
A. Jiménez-Losada
Keyword(s):  
Partition Function ◽  
Shapley Value ◽  
Cooperative Games ◽  
Function Form ◽  
Original Game ◽  
Classic Result ◽  
The Shapley Value ◽  
Partition Function Form Games ◽  
Partition Function Form

AbstractIn this paper an order on the set of embedded coalitions is studied in detail. This allows us to define new notions of superaddivity and convexity of games in partition function form which are compared to other proposals in the literature. The main results are two characterizations of convexity. The first one uses non-decreasing contributions to coalitions of increasing size and can thus be considered parallel to the classic result for cooperative games without externalities. The second one is based on the standard convexity of associated games without externalities that we define using a partition of the player set. Using the later result, we can conclude that some of the generalizations of the Shapley value to games in partition function form lie within the cores of specific classic games when the original game is convex.

A Note on a Class of Solutions for Games with Externalities Generalizing the Shapley Value

2015 ◽  
Vol 17 (03) ◽  
pp. 1550003 ◽  
Author(s):  
Joss Sánchez-Pérez
Keyword(s):  
Partition Function ◽  
Shapley Value ◽  
Complete Characterization ◽  
Function Form ◽  
Characterization Result ◽  
The Shapley Value ◽  
Games With Externalities ◽  
Partition Function Form

In this paper we study a family of extensions of the Shapley value for games in partition function form with n players. In particular, we provide a complete characterization for all linear, symmetric, efficient and null solutions in these environments. Finally, we relate our characterization result with other ways to extend the Shapley value in the literature.

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).

COMPROMISING IN PARTITION FUNCTION FORM GAMES AND COOPERATION IN PERFECT EXTENSIVE FORM GAMES

2006 ◽  
Vol 08 (03) ◽  
pp. 329-338
Author(s):  
E. FUKUDA ◽  
S. H. TIJS ◽  
R. BRÂNZEI ◽  
S. MUTO
Keyword(s):  
Partition Function ◽  
Axiomatic Characterization ◽  
Perfect Information ◽  
Function Form ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Compromise Value ◽  
Partition Function Form Games ◽  
Partition Function Form

In this paper reasonable payoff intervals for players in a game in partition function form (p.f.f. game) are introduced and used to define the notion of compromisable p.f.f. game. For a compromisable p.f.f. game a compromise value is defined for which an axiomatic characterization is provided. Also a generic subclass of games in extensive form of perfect information without chance moves is introduced. For this class of perfect extensive form games there is a natural credible way to define a p.f.f. game if the players consider cooperation. It turns out that the p.f.f. games obtained in this way are compromisable.

scholarly journals THE CONSENSUS VALUE FOR GAMES IN PARTITION FUNCTION FORM

2007 ◽  
Vol 09 (03) ◽  
pp. 437-452 ◽  
Author(s):  
YUAN JU
Keyword(s):  
Partition Function ◽  
Unique Function ◽  
Function Form ◽  
Property A ◽  
Transfer Property ◽  
Consensus Value ◽  
Null Player ◽  
Partition Function Form Games ◽  
Partition Function Form ◽  
Axiomatic Extension

This paper studies a procedural and axiomatic extension of the consensus value [cf. Ju et al. (2007)] to the class of partition function form games. This value is characterized as the unique function that satisfies efficiency, complete symmetry, the quasi-null player property and additivity. By means of the transfer property, a second characterization is provided. Moreover, it is shown that the consensus value satisfies individual rationality under a superadditivity condition, and well balances the tradeoff between coalitional effects and externality effects. In this respect, explicit differences with other solution concepts are indicated.

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