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.

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.

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.

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 CORE AND CONSISTENCY PROPERTIES: A GENERAL CHARACTERISATION

2001 ◽  
Vol 03 (02n03) ◽  
pp. 175-187 ◽  
Author(s):  
YUKIHIKO FUNAKI ◽  
TAKEHIKO YAMATO
Keyword(s):  
General Theorem ◽  
General Definition ◽  
Tu Games ◽  
The Core ◽  
Special Cases ◽  
Reduced Games ◽  
Definition Of ◽  
Consistency Properties

In this paper, we unify various axiomatisations of the core of TU games by means of consistency with respect to different definitions of reduced games. First, we introduce a general definition of reduced games including the reduced games due to Davis and Maschler (1965), Moulin (1985), and Funaki (1995) as special cases. Then, we provide a general theorem from which the characterisations due to Peleg (1986), Tadenuma (1992), and Funaki (1995) can be obtained. Our general theorem clarifies how the three characterisations of the core differ and are related.

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 Monotonicity and Weighted Prenucleoli: A Characterization Without Consistency

2020 ◽  
Vol 45 (3) ◽  
pp. 1056-1068
Author(s):  
Pedro Calleja ◽  
Francesc Llerena ◽  
Peter Sudhölter
Keyword(s):  
Regular System ◽  
Necessary Condition ◽  
Transferable Utility ◽  
Tu Games ◽  
Scale Covariance ◽  
Per Capita ◽  
Arbitrary Weight ◽  
Translation Covariance ◽  
Equal Surplus Division ◽  
Aggregate Monotonicity

A solution on a set of transferable utility (TU) games satisfies strong aggregate monotonicity (SAM) if every player can improve when the grand coalition becomes richer. It satisfies equal surplus division (ESD) if the solution allows the players to improve equally. We show that the set of weight systems generating weighted prenucleoli that satisfy SAM is open, which implies that for weight systems close enough to any regular system, the weighted prenucleolus satisfies SAM. We also provide a necessary condition for SAM for symmetrically weighted nucleoli. Moreover, we show that the per capita nucleolus on balanced games is characterized by single-valuedness (SIVA), translation covariance (TCOV) and scale covariance (SCOV), and equal adjusted surplus division (EASD), a property that is comparable to but stronger than ESD. These properties together with ESD characterize the per capita prenucleolus on larger sets of TU games. EASD and ESD can be transformed to independence of (adjusted) proportional shifting, and these properties may be generalized for arbitrary weight systems p to I(A)Sp. We show that the p-weighted prenucleolus on the set of balanced TU games is characterized by SIVA, TCOV, SCOV, and IASp and on larger sets by additionally requiring ISp.

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.

COALITIONAL BELIEFS IN COURNOT OLIGOPOLY TU GAMES

2013 ◽  
Vol 15 (01) ◽  
pp. 1350004 ◽  
Author(s):  
PARASKEVAS V. LEKEAS
Keyword(s):  
Computational Complexity ◽  
Cooperative Games ◽  
Cournot Competition ◽  
Cournot Oligopoly ◽  
Tu Game ◽  
Main Interest ◽  
Tu Games ◽  
Strategic Interest

In cooperative games, due to computational complexity issues, deviant agents are not able to base their behavior on the outsiders' status but have to follow certain beliefs as to how it is in their strategic interest to act. This behavior constitutes the main interest of this paper. To this end, we quantify and characterize the set of coalitional beliefs that support cooperation of such agents. Assuming that they are engaged in a differentiated Cournot competition, for every belief of the deviants we define a TU-game, the solution to which characterizes the set of coalitional beliefs that support core nonemptiness. For this we fix the number of coalitions that deviants S will face to, say, j in number and introduce the notion of j-belief of S as the least number of coalitions into which the outsiders N\S will reorganize. We then define for every j-belief a TU-game and the j-belief core of it. We prove that the worth of S is minimized when the n – s agents split approximately equally among the j coalitions, while the worth of S is maximized when j – 1 agents have one member and one coalition has n – s – (j – 1) members. Given the above, we prove that when goods are substitutes, the j-belief core is nonempty, provided that S believe the N\S will form a sufficiently large number of coalitions, while when goods are complements, the j-belief core is nonempty irrespective of the beliefs of the agents in S. Finally, in the case of homogeneous goods we prove that the j-belief core is nonempty and depends only on the number of the outsider coalitions and not on their size.

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