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.

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.

A NECESSARY AND SUFFICIENT CONDITION FOR THE NON-EMPTINESS OF THE SOCIALLY STABLE CORE IN STRUCTURED TU-GAMES

2009 ◽  
Vol 11 (03) ◽  
pp. 383-389
Author(s):  
JUAN CARLOS CESCO
Keyword(s):  
Sufficient Condition ◽  
Transferable Utility ◽  
Tu Game ◽  
Necessary And Sufficient Condition ◽  
Tu Games ◽  
Classical Condition ◽  
Stable Core ◽  
Necessary And Sufficient

In this note we provide a neccesary and sufficient condition for the non-emptiness of the socially stable core of a general structured TU-game which resembles closely the classical condition of balancedness given by Bondareva (1963) and Shapley (1967) to guarantee the non-emptiness of the classical core. Structured games have been introduced in Herings et al. (2007a) and more recently, in Herings et al. (2007b), studied in the framework of games with transferable utility. In the latter paper, the authors provide suffcient conditions for the non-emptiness of the socially stable core, but up to now, no necessary and sufficient condition is known.

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.

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 POSITIVE PREKERNEL OF A COOPERATIVE GAME

2000 ◽  
Vol 02 (04) ◽  
pp. 287-305 ◽  
Author(s):  
PETER SUDHÖLTER ◽  
BEZALEL PELEG
Keyword(s):  
Cooperative Game ◽  
Weak Version ◽  
Transferable Utility ◽  
Bargaining Set ◽  
The Core ◽  
Reduced Game ◽  
Positive Kernel ◽  
Game Property ◽  
Transferable Utility Games

The positive prekernel, a solution of cooperative transferable utility games, is introduced. We show that this solution inherits many properties of the prekernel and of the core, which are both sub-solutions. It coincides with its individually rational variant, the positive kernel, when applied to any zero-monotonic game. The positive (pre)kernel is a sub-solution of the reactive (pre)bargaining set. We prove that the positive prekernel on the set of games with players belonging to a universe of at least three possible members can be axiomatized by non-emptiness, anonymity, reasonableness, the weak reduced game property, the converse reduced game property, and a weak version of unanimity for two-person games.

THE EXTENSION OF DUTTA–RAY'S SOLUTION TO CONVEX NTU GAMES

2010 ◽  
Vol 12 (04) ◽  
pp. 339-361
Author(s):  
ELENA YANOVSKAYA
Keyword(s):  
Axiomatic Characterization ◽  
Convexity Property ◽  
Tu Games ◽  
Ntu Games ◽  
The Core ◽  
Egalitarian Solution

The egalitarian solution for the class of convex TU games was defined by Dutta and Ray [1989] and axiomatized by Dutta 1990. An extension of this solution — the egalitarian split-off set (ESOS) — to the class of non-levelled NTU games is proposed. On the class of TU games it coincides with the egalitarian split-off set [Branzei et al. 2006]. The proposed extension is axiomatized as the maximal (w.r.t. inclusion) solution satisfying consistency à la Hart–Mas-Colell and agreeing with the solution of constrained egalitarianism for arbitrary two-person games. For ordinal convex NTU games the ESOS turns out to be single-valued and contained in the core. The totally cardinal convexity property of NTU games is defined. For the class of ordinal and total cardinal convex NTU games an axiomatic characterization of the Dutta–Ray solution with the help of Peleg consistency is given.

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 Hart–Mas-Colell consistency and the core in convex games

2021 ◽  
Author(s):  
Bas Dietzenbacher ◽  
Peter Sudhölter
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Individual Rationality ◽  
Transferable Utility ◽  
Convex Games ◽  
The Core ◽  
The Shapley Value ◽  
Scale Covariance

AbstractThis paper formally introduces Hart–Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covariance, superadditivity, weak Hart–Mas-Colell consistency, and converse Hart–Mas-Colell consistency. This family consists of (a) the Shapley value, (b) all homothetic images of the core with the Shapley value as center of homothety and with positive ratios of homothety not larger than one, and (c) their relative interiors.

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.

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)).

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