scholarly journals Associated consistency and values for TU games

2010 ◽  
Vol 39 (3) ◽  
pp. 467-482 ◽  
Author(s):  
Theo S. H. Driessen
Keyword(s):  
Tu Games ◽  
Associated Consistency

scholarly journals Associated Consistency Characterization of Two Linear Values for Tu Games by Matrix Approach

2012 ◽  
Author(s):  
Genjiu Xu ◽  
René van den Brink ◽  
Gerard van der Laan ◽  
Hao Sun
Keyword(s):  
Matrix Approach ◽  
Tu Games ◽  
Associated Consistency

POTENTIAL IN MULTI-CHOICE COOPERATIVE TU GAMES

2008 ◽  
Vol 25 (05) ◽  
pp. 591-611 ◽  
Author(s):  
YAN-AN HWANG ◽  
YU-HSIEN LIAO
Keyword(s):  
Transferable Utility ◽  
Tu Games ◽  
Cooperative Tu Games ◽  
All Solutions ◽  
The Family ◽  
Balanced Contributions ◽  
Associated Consistency

This paper is devoted to the study of solutions for multi-choice transferable-utility (TU) games which admit a potential, such as the potential associated with a solution in the context of multi-choice TU games. Several axiomatizations of the family of all solutions that admit a potential are offered and, as a main result, it is shown that each of these solutions can be obtained by applying the weighted associated consistent value proposed in this paper to an appropriately modified game. We also characterize the weighted associated consistent value by means of the weighted balanced contributions and the associated consistency.

scholarly journals Characterizations of Three Linear Values for TU Games by Associated Consistency: Simple Proofs Using the Jordan Normal Form

2016 ◽  
Vol 18 (01) ◽  
pp. 1650003 ◽  
Author(s):  
Sylvain Béal ◽  
Eric Rémila ◽  
Philippe Solal
Keyword(s):  
Normal Form ◽  
Cooperative Games ◽  
Matrix Analysis ◽  
Transferable Utility ◽  
Jordan Normal Form ◽  
Linear Transformations ◽  
Tu Games ◽  
The Matrix ◽  
Matrix Expression ◽  
Associated Consistency

This paper studies values for cooperative games with transferable utility. Numerous such values can be characterized by axioms of [Formula: see text]-associated consistency, which require that a value is invariant under some parametrized linear transformation [Formula: see text] on the vector space of cooperative games with transferable utility. Xu et al. [(2008) Linear Algebr. Appl. 428, 1571–1586; (2009) Linear Algebr. Appl. 430, 2896–2897] Xu et al. [(2013) Linear Algebr. Appl. 439, 2205–2215], Hamiache [(2010) Int. Game Theor. Rev. 12, 175–187] and more recently Xu et al. [(2015) Linear Algebr. Appl. 471, 224–240] follow this approach by using a matrix analysis. The main drawback of these articles is the heaviness of the proofs to show that the matrix expression of the linear transformations is diagonalizable. By contrast, we provide quick proofs by relying on the Jordan normal form of the previous matrix.

scholarly journals Associated consistency characterization of two linear values for TU games by matrix approach

2015 ◽  
Vol 471 ◽  
pp. 224-240 ◽  
Author(s):  
Genjiu Xu ◽  
René van den Brink ◽  
Gerard van der Laan ◽  
Hao Sun
Keyword(s):  
Matrix Approach ◽  
Tu Games ◽  
Associated Consistency

THE RIVER SHARING PROBLEM: A SURVEY

2013 ◽  
Vol 15 (03) ◽  
pp. 1340016 ◽  
Author(s):  
SYLVAIN BEAL ◽  
AMANDINE GHINTRAN ◽  
ERIC REMILA ◽  
PHILIPPE SOLAL
Keyword(s):  
Optimal Allocation ◽  
Market Mechanism ◽  
Tu Game ◽  
Tu Games ◽  
Cooperative Tu Game ◽  
Fair Distribution

The river sharing problem deals with the fair distribution of welfare resulting from the optimal allocation of water among a set of riparian agents. Ambec and Sprumont [Sharing a river, J. Econ. Theor. 107, 453–462] address this problem by modeling it as a cooperative TU-game on the set of riparian agents. Solutions to that problem are reviewed in this article. These solutions are obtained via an axiomatic study on the class of river TU-games or via a market mechanism.

The SD-prenucleolus for TU games

2014 ◽  
Vol 80 (3) ◽  
pp. 307-327 ◽  
Author(s):  
J. Arin ◽  
I. Katsev
Keyword(s):  
Tu Games

1-concave basis for TU games and the library game

Top ◽  
2010 ◽  
Vol 20 (3) ◽  
pp. 578-591 ◽  
Author(s):  
Theo S. H. Driessen ◽  
Anna B. Khmelnitskaya ◽  
Jordi Sales
Keyword(s):  
Tu Games

Effects of Players’ Nullification and Equal (Surplus) Division Values

2018 ◽  
Vol 20 (01) ◽  
pp. 1750029 ◽  
Author(s):  
Takumi Kongo
Keyword(s):  
The Other ◽  
Equal Division ◽  
Transferable Utility ◽  
Tu Games ◽  
Axiomatic Characterizations ◽  
The Difference ◽  
Monotonicity Axioms ◽  
Equal Surplus Division

We provide axiomatic characterizations of the solutions of transferable utility (TU) games on the fixed player set, where at least three players exist. We introduce two axioms on players’ nullification. One axiom requires that the difference between the effect of a player’s nullification on the nullified player and on the others is relatively constant if all but one players are null players. Another axiom requires that a player’s nullification affects equally all of the other players. These two axioms characterize the set of all affine combinations of the equal surplus division and equal division values, together with the two basic axioms of efficiency and null game. By replacing the first axiom on players’ nullification with appropriate monotonicity axioms, we narrow down the solutions to the set of all convex combinations of the two values, or to each of the two values.

scholarly journals The Fairness of Solidarity Bills under the Solidarity Value of Nowak and Radzik

Game Theory ◽  
2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Lawrence Diffo Lambo ◽  
Pierre Wambo
Keyword(s):  
Shapley Value ◽  
Real World ◽  
Side Effect ◽  
Tu Games ◽  
Unwanted Side Effect ◽  
The Disabled ◽  
Threshold Position ◽  
To Receive

The solidarity value is a variant of the well-known Shapley value in which some sense of solidarity between the players is implemented allowing the disabled to receive help from the fortunate ones. We investigate on how fairly solidarity expenses are shared. We discuss the unwanted side effect of someone paying undue solidarity contributions as far as reversing his condition from a privileged to a needy person. A deeper case study is conducted for two classes of TU games that we obtain by modeling two real world business contexts. Here, we trace all player to player transfers of funds that arise when solidarity actions are processed, and we answer the question of who settles the solidarity bills. Also, we obtain the threshold position of a player below which he gets solidarity help, but above which he instead pays out donation.

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