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.

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.

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

CONVEXITY OF THE "AIRPORT PROFIT GAME" AND k-CONVEXITY OF THE "BANKRUPTCY GAME"

2013 ◽  
Vol 15 (04) ◽  
pp. 1340022 ◽  
Author(s):  
DONGSHUANG HOU ◽  
THEO DRIESSEN
Keyword(s):  
Cost Function ◽  
Minimization Problem ◽  
Gap Function ◽  
Bankruptcy Games ◽  
Equivalent Properties ◽  
Bankruptcy Game

The topic is two-fold. First, we prove the convexity of Owen's Airport Profit Game (inclusive of revenues and costs). As an adjunct, we characterize the class of 1-convex Airport Profit Games by equivalent properties of the corresponding cost function. Second, we classify the class of 1-convex Bankruptcy Games by solving a minimization problem of its corresponding gap function.

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.

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)).

PROJECT MANAGEMENT GAMES

2011 ◽  
Vol 13 (03) ◽  
pp. 281-300 ◽  
Author(s):  
IMMA CURIEL
Keyword(s):  
Project Management ◽  
Completion Time ◽  
Cooperative Game Theory ◽  
Sufficient Conditions ◽  
Extreme Points ◽  
Convex Games ◽  
The Core ◽  
Management Games ◽  
Big Boss Games ◽  
Necessary And Sufficient

This paper studies situations in which companies can cooperate in order to decrease the earliest completion time of a project that consists of several tasks. This is beneficial for the client who wants the project to be completed as early as possible. The client is willing to pay more for an earlier completion time. The total payoff must be allocated among the companies that cooperate. Cooperative game theory is used to model this situation. Conditions for the core of the game to be nonempty are derived. We study a class of project management games for which necessary and sufficient conditions for the nonemptiness of the core can be derived. We will show that a subset of the set of balanced project management games can be partitioned into a class of 1-convex games and a class of big boss games. Expressions for the extreme points of the core, the τ-value, the nucleolus, and the Shapley-value of games in these two classes are derived.

scholarly journals The core and the steady bargaining set for convex games

2017 ◽  
Vol 47 (1) ◽  
pp. 35-54
Author(s):  
Josep Maria Izquierdo ◽  
Carles Rafels
Keyword(s):  
Convex Games ◽  
Bargaining Set ◽  
The Core

USING THE ASPIRATION CORE TO PREDICT COALITION FORMATION

2012 ◽  
Vol 14 (01) ◽  
pp. 1250004 ◽  
Author(s):  
CAMELIA BEJAN ◽  
JUAN CAMILO GÓMEZ
Keyword(s):  
Nash Equilibrium ◽  
Coalition Formation ◽  
Solution Concept ◽  
Transferable Utility ◽  
Tu Game ◽  
Subgame Perfect Nash Equilibrium ◽  
The Core ◽  
Core Solution ◽  
Aspiration Core ◽  
Overlapping Coalitions

This work uses the defining principles of the core solution concept to determine not only payoffs but also coalition formation. Given a cooperative transferable utility (TU) game, we propose two noncooperative procedures that in equilibrium deliver a natural and nonempty core extension, the aspiration core, together with the supporting coalitions it implies. As expected, if the cooperative game is balanced, the grand coalition forms. However, if the core is empty, other coalitions arise. Following the aspiration literature, not only partitions but also overlapping coalition configurations are allowed. Our procedures interpret this fact in different ways. The first game allows players to participate with a fraction of their time in more than one coalition, while the second assigns probabilities to the formation of potentially overlapping coalitions. We use the strong Nash and subgame perfect Nash equilibrium concepts.

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