THE EXTENDED CORE OF A COOPERATIVE NTU GAME

2010 ◽  
Vol 12 (03) ◽  
pp. 263-274 ◽  
Author(s):  
HANS KEIDING ◽  
YAROSLAVNA PANKRATOVA
Keyword(s):  
Solution Concept ◽  
Tu Games ◽  
Ntu Games ◽  
The Core ◽  
Ntu Game ◽  
Straightforward Generalization

In this paper we propose an extension of the core of NTU games from its domain to a larger set of games satisfying a few conditions of well-behavedness. The solution concept is a rather straightforward generalization of the extended core of TU games introduced by Gomez [2003] and is shown to have similar properties. Also, a set of axioms for solutions of NTU games is presented which characterizes the extended core.

scholarly journals On Bargaining Sets of Convex NTU Games

2015 ◽  
Vol 17 (04) ◽  
pp. 1550008 ◽  
Author(s):  
Bezalel Peleg ◽  
Peter Sudhölter
Keyword(s):  
Bargaining Set ◽  
Ntu Games ◽  
The Core ◽  
Ntu Game ◽  
Bargaining Sets

We show that the Aumann–Davis–Maschler bargaining set and the Mas-Colell bargaining set of a non-leveled NTU game that is either ordinal convex or coalition merge convex coincides with the core of the game. Moreover, we show by means of an example that the foregoing statement may not be valid if the NTU game is marginal convex.

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.

CONSISTENCY IN VALUES

2004 ◽  
Vol 06 (04) ◽  
pp. 461-473 ◽  
Author(s):  
GUILLERMO OWEN
Keyword(s):  
Shapley Value ◽  
Solution Concept ◽  
Tu Games ◽  
Ntu Games ◽  
Reduced Game ◽  
Reduced Games ◽  
Shapley Values ◽  
Consistent Solution ◽  
Person Game ◽  
Reasonable Behavior

Given an n-person game (N, v), a reduced game (T, vT) is the game obtained if some subset T of the players assumes reasonable behavior on the part of the remaining players and uses that as a given so as to bargain within T. This "reasonable" behavior on the part of N-T must be defined in terms of some solution concept, ϕ, and so the reduced game depends on ϕ. Then, the solution concept ϕ is said to be consistent if it gives the same result to the reduced games as it does to the original game. It turns out that, given a symmetry condition on two-person games, the Shapley value is the only consistent solution on the space of TU games. Modification of some definitions will instead give the prekernel, the prenucleolus, or the weighted Shapley values. A generalization to NTU games is given. This works well for the class of hyperplane games, but not quite so well for general games.

THE EGALITARIAN NON-k-AVERAGED CONTRIBUTION (ENkAC-) VALUE FOR TU-GAMES

1999 ◽  
Vol 01 (01) ◽  
pp. 45-61 ◽  
Author(s):  
TSUNEYUKI NAMEKATA ◽  
THEO S. H. DRIESSEN
Keyword(s):  
Solution Concept ◽  
Sufficient Condition ◽  
Individual Contribution ◽  
Transferable Utility ◽  
Tu Games ◽  
The Core ◽  
Centre Of Gravity ◽  
Transferable Utility Game ◽  
Individual Contributions ◽  
Transferable Utility Games

This paper deals in a unified way with the solution concepts for transferable utility games known as the Centre of the Imputation Set value (CIS-value), the Egalitarian Non-Pairwise-Averaged Contribution value (ENPAC-value) and the Egalitarian Non-Separable Contribution value (ENSC-value). These solutions are regarded as the egalitarian division of the surplus of the overall profits after each participant is conceded to get his individual contribution specified in a respective manner. We offer two interesting individual contributions (lower- and upper-k-averaged contribution) based on coalitions of size k(k ∈ {1,…,n-1}) and introduce a new solution concept called the Egalitarian Non-k-Averaged Contribution value ( EN k AC -value). CIS-, ENPAC- and ENSC-value are the same as EN 1 AC -, EN n-2 AC - and EN n-1 AC -value respectively. It turns out that the lower- and the upper-k-averaged contribution form a lower- and an upper-bound of the Core respectively. The Shapley value is the centre of gravity of n-1 points; EN 1 AC -,…, EN n-1 AC -value. EN k AC -value of the dual game is equal to EN n-k AC -value of the original game. We provide a sufficient condition on the transferable utility game to guarantee that the EN k AC -value coincides with the well-known solution called prenucleolus. The condition requires that the largest excesses at the EN k AC -value are attained at the k-person coalitions, whereas the excesses of k-person coalitions at the EN k AC -value do not differ.

scholarly journals The Core of Large Differentiable TU Games

2001 ◽  
Vol 100 (2) ◽  
pp. 235-273 ◽  
Author(s):  
Larry G. Epstein ◽  
Massimo Marinacci
Keyword(s):  
Tu Games ◽  
The Core

A NOTE ON CHARACTERIZING CORE STABILITY WITH FUZZY GAMES

2011 ◽  
Vol 13 (01) ◽  
pp. 105-118 ◽  
Author(s):  
EVAN SHELLSHEAR
Keyword(s):  
Cooperative Game ◽  
Core Stability ◽  
Original Game ◽  
Tu Games ◽  
The Core ◽  
Cooperative Tu Games ◽  
Fuzzy Games ◽  
The Stability

This paper investigates core stability of cooperative (TU) games via a fuzzy extension of the totally balanced cover of a cooperative game. The stability of the core of the fuzzy extension of a game, the concave extension, is shown to reflect the core stability of the original game and vice versa. Stability of the core is then shown to be equivalent to the existence of an equilibrium of a certain correspondence.

ON BARGAINING SETS IN SYMMETRIC GAMES

2007 ◽  
Vol 09 (02) ◽  
pp. 199-213 ◽  
Author(s):  
MARC MEERTENS ◽  
J. A. M. POTTERS ◽  
J. H. REIJNIERSE
Keyword(s):  
Bargaining Set ◽  
Tu Games ◽  
The Core ◽  
Symmetric Games ◽  
Bargaining Sets ◽  
Additional Assumptions

The paper investigates under which additional assumptions the bargaining set, the reactive bargaining set or the semireactive bargaining set coincides with the core on the class of symmetric TU-games. Furthermore, we give an example which illustrates that the property 'the bargaining set coincides with the core' is not a prosperity property.

Sequentially compatible payoffs and the core in TU-games

2005 ◽  
Vol 50 (3) ◽  
pp. 318-330 ◽  
Author(s):  
Josep M. Izquierdo ◽  
Francesc Llerena ◽  
Carles Rafels
Keyword(s):  
Tu Games ◽  
The Core
Sign in / Sign up

Export Citation Format

Share Document