A Shapley Value Algorithm for Games in Partition Function Form

2013 ◽  
pp. 63-83
Keyword(s):  
Partition Function ◽  
Shapley Value ◽  
Function Form ◽  
Partition Function Form

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).

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.

Book Reviews

2014 ◽  
Vol 52 (1) ◽  
pp. 213-215
Keyword(s):  
Partition Function ◽  
Cooperative Games ◽  
Bargaining Power ◽  
Nash Bargaining ◽  
Function Form ◽  
Drexel University ◽  
New Concepts ◽  
University Of Manchester ◽  
Transferable Utility Games ◽  
Partition Function Form

Omer Edhan of University of Manchester reviews, “Value Solutions in Cooperative Games” by Roger A. McCain. The Econlit abstract of this book begins: “Presents new concepts for cooperative game theory, with a particular focus on solutions that determine the distribution of a coalitional surplus among the members of the coalition. Discusses value solutions for superadditive transferable utility games in coalition function form; Zeuthen–Nash bargaining; nontransferable utility games and games in partition function form; a Shapley value algorithm for games in partition function form; extension of the nucleolus to nontransferable utility games in partition function form; a core imputation with variable bargaining power; bargaining power biform games; intertemporal cooperative games—a sketch of a theory; and a theory of enterprise. McCain is at Drexel University.”

THE CLASS OF EFFICIENT LINEAR SYMMETRIC VALUES FOR GAMES IN PARTITION FUNCTION FORM

2009 ◽  
Vol 11 (03) ◽  
pp. 369-382 ◽  
Author(s):  
L. HERNÁNDEZ-LAMONEDA ◽  
J. SÁNCHEZ-PÉREZ ◽  
F. SÁNCHEZ-SÁNCHEZ
Keyword(s):  
Partition Function ◽  
Efficient Solutions ◽  
Function Form ◽  
Additional Axiom ◽  
Partition Function Form

In this paper we study linear symmetric solutions for the space of games in partition function form with n players. In particular, we provide an expression for all linear, symmetric and efficient solutions. Furthermore, adding an additional axiom, we identify a unique value satisfying these properties.

The core of a strategic game

2018 ◽  
Vol 19 (1) ◽  
Author(s):  
Parkash Chander
Keyword(s):  
Partition Function ◽  
Cooperative Game ◽  
Unique Equilibrium ◽  
Strategic Game ◽  
Function Form ◽  
Equilibrium Outcome ◽  
Cooperative Solution ◽  
Payoff Vector ◽  
The Core ◽  
Partition Function Form

AbstractIn this paper, I introduce and study the $\gamma$-core of a general strategic game. I first show that the $\gamma$-core of an arbitrary strategic game is smaller than the conventional $\alpha$- and $\beta$- cores. I then consider the partition function form of a general strategic game and show that a prominent class of partition function games admit nonempty $\gamma$-cores. Finally, I show that each $\gamma$-core payoff vector (a cooperative solution) can be supported as an equilibrium outcome of an intuitive non-cooperative game and the grand coalition is the unique equilibrium outcome if and only if the $\gamma$-core is non-empty.

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