The simplified modified nucleolus of a cooperative TU-game

Top ◽  
2010 ◽  
Vol 19 (1) ◽  
pp. 150-166 ◽  
Author(s):  
Svetlana Tarashnina
Keyword(s):  
Tu Game ◽  
Cooperative Tu Game

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.

LARGENESS OF THE CORE OF k-CONVEX SYMMETRIC GAMES

2013 ◽  
Vol 15 (04) ◽  
pp. 1340023
Author(s):  
AMIT K BISWAS
Keyword(s):  
Core Structure ◽  
Tu Game ◽  
Convex Games ◽  
Large Core ◽  
Convex Game ◽  
The Core ◽  
Symmetric Games ◽  
Cooperative Tu Game

A cooperative TU game is said to posses a large core as defined by Sharkey [1982] if for every acceptable vector there is a smaller core vector in the game. This paper is devoted to characterization(s) of largeness of the core of a subclass of games known as k-convex games (containing the convex games in case k = n). The k-convex games were defined by Driessen [1988] because of the core structure they possess, which is the same as that of a suitably defined convex game. The main goal is to show that the totally balanced symmetric k-convex games possess a large core if and only if the game is convex.

A natural selection from the core of a TU game: the core-center

2007 ◽  
Vol 36 (1) ◽  
pp. 27-46 ◽  
Author(s):  
Julio González-Díaz ◽  
Estela Sánchez-Rodríguez
Keyword(s):  
Natural Selection ◽  
Tu Game ◽  
The Core

NONEMPTY CORE-TYPE SOLUTIONS OVER BALANCED COALITIONS IN TU-GAMES

2012 ◽  
Vol 14 (03) ◽  
pp. 1250018 ◽  
Author(s):  
JUAN C. CESCO
Keyword(s):  
Equal Opportunity ◽  
Axiomatic Characterization ◽  
Individual Rationality ◽  
Transferable Utility ◽  
Tu Game ◽  
Tu Games ◽  
Additional Axiom ◽  
Game Property ◽  
Minimality Property ◽  
New Framework

In this paper we introduce two related core-type solutions for games with transferable utility (TU-games) the [Formula: see text]-core and the [Formula: see text]-core. The elements of the solutions are pairs [Formula: see text] where x, as usual, is a vector representing a distribution of utility and [Formula: see text] is a balanced family of coalitions, in the case of the [Formula: see text]-core, and a minimal balanced one, in the case of the [Formula: see text]-core, describing a plausible organization of the players to achieve the vector x. Both solutions extend the notion of classical core but, unlike it, they are always nonempty for any TU-game. For the [Formula: see text]-core, which also exhibits a certain kind of "minimality" property, we provide a nice axiomatic characterization in terms of the four axioms nonemptiness (NE), individual rationality (IR), superadditivity (SUPA) and a weak reduced game property (WRGP) (with appropriate modifications to adapt them to the new framework) used to characterize the classical core. However, an additional axiom, the axiom of equal opportunity is required. It roughly states that if [Formula: see text] belongs to the [Formula: see text]-core then, any other admissible element of the form [Formula: see text] should belong to the solution too.

scholarly journals THE DUTTA-RAY SOLUTION ON THE CLASS OF CONVEX GAMES: A GENERALIZATION AND MONOTONICITY PROPERTIES

2005 ◽  
Vol 07 (04) ◽  
pp. 431-442 ◽  
Author(s):  
JENS LETH HOUGAARD ◽  
BEZALEL PELEG ◽  
LARS PETER ØSTERDAL
Keyword(s):  
Tu Game ◽  
Convex Games ◽  
Population Monotonicity ◽  
The Core ◽  
Maximal Solutions ◽  
Monotonicity Properties

This paper considers generalized Lorenz-maximal solutions in the core of a convex TU-game and demonstrates that such solutions satisfy coalitional monotonicity and population monotonicity.

A new axiomatization of a class of equal surplus division values for TU games

2018 ◽  
Vol 52 (3) ◽  
pp. 935-942 ◽  
Author(s):  
Xun-Feng Hu ◽  
Deng-Feng Li
Keyword(s):  
Equal Division ◽  
Tu Game ◽  
Tu Games ◽  
Special Cases ◽  
Equal Surplus Division

In this paper, we propose a variation of weak covariance named as non-singleton covariance, requiring that changing the worth of a non-singleton coalition in a TU game affects the payoffs of all players equally. We establish that this covariance is characteristic for the convex combinations of the equal division value and the equal surplus division value, together with efficiency and a one-parameterized axiom treating a particular kind of players specially. As special cases, parallel axiomatizations of the two values are also provided.

The Need for Permission, the Power to Enforce, and Duality in Cooperative Games with a Hierarchy

2016 ◽  
Vol 18 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Frank Huettner ◽  
Harald Wiese
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Transferable Utility ◽  
Tu Game ◽  
Tu Games ◽  
Permission Value

A cooperative game with transferable utility (TU game) captures a situation in which players can achieve certain payoffs by cooperating. We assume that the players are part of a hierarchy. In the literature, this invokes the assumption that subordinates cannot cooperate without the permission of their superiors. Instead, we assume that superiors can force their subordinates to cooperate. We show how both notions correspond to each other by means of dual TU games. This way, we capture the idea that a superiors’ ability to enforce cooperation can be seen as the ability to neutralize her subordinate’s threat to abstain from cooperation. Moreover, we introduce the coercion value for games with a hierarchy and provide characterizations thereof that reveal the similarity to the permission value.

U-CYCLES IN n-PERSON TU-GAMES WITH ONLY 1, n - 1 AND n-PERSON PERMISSIBLE COALITIONS

2006 ◽  
Vol 08 (03) ◽  
pp. 355-368 ◽  
Author(s):  
JUAN CARLOS CESCO ◽  
ANA LUCÍA CALÍ
Keyword(s):  
Characterization Theorem ◽  
Tu Game ◽  
Transfer Scheme ◽  
Tu Games ◽  
The Core ◽  
Core Of A Game ◽  
Necessary And Sufficient

It has been recently proved that the non-existence of certain type of cycles of pre-imputation, fundamental cycles, is equivalent to the balancedness of a TU-games (Cesco (2003)). In some cases, the class of fundamental cycles can be narrowed and still obtain a characterization theorem. In this paper we prove that existence of maximal U-cycles, which are related to a transfer scheme designed for computing a point in the core of a game, is condition necessary and sufficient for a TU-game be non-balanced, provided n - 1 and n-person are the only coalitions with non-zero value. These games are strongly related to games with only 1, n - 1 and n-person permissible coalitions (Maschler (1963)).

scholarly journals Bankruptcy Problem Allocations and the Core of Convex Games

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
William Olvera-Lopez ◽  
Francisco Sanchez-Sanchez ◽  
Iván Tellez-Tellez
Keyword(s):  
Convex Functions ◽  
Tu Game ◽  
Convex Games ◽  
Bankruptcy Problem ◽  
Bankruptcy Problems ◽  
The Core ◽  
Bankruptcy Games ◽  
Bankruptcy Game

A well-known result related to bankruptcy problems establishes that a vector is a bankruptcy allocation if and only if it belongs to the core of the associated O’Neill’s bankruptcy game. In this paper we show that this game is precisely the unique TU-game based on convex functions that satisfies the previous result. In addition, given a bankruptcy problem, we show a way for constructing bankruptcy games such that the set of bankruptcy allocations is a subset of their core or their core is a subset of the set of bankruptcy allocations. Also, we show how these results can be applied for finding new bankruptcy solutions.

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