Weighted values and the core in NTU games

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.

Download Full-text

An Implementation of the Core of NTU-Games

Game Theoretical Applications to Economics and Operations Research - Theory and Decision Library ◽

10.1007/978-1-4757-2640-4_9 ◽

1997 ◽

pp. 105-111

Author(s):

Gustavo Bergantiños ◽

Jos A. M. Potters

Keyword(s):

Ntu Games ◽

The Core

Download Full-text

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

International Game Theory Review ◽

10.1142/s0219198910002714 ◽

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.

Download Full-text

Two characterizations of the consistent egalitarian solution and of the core on NTU games

Mathematical Methods of Operations Research ◽

10.1007/s00186-006-0100-6 ◽

2006 ◽

Vol 64 (3) ◽

pp. 557-568 ◽

Cited By ~ 3

Author(s):

Yan-An Hwang

Keyword(s):

Ntu Games ◽

The Core ◽

Egalitarian Solution

Download Full-text

The Core of NTU Games

Introduction to the Theory of Cooperative Games - Theory and Decision Library ◽

10.1007/978-3-540-72945-7_12 ◽

2007 ◽

pp. 213-234

Keyword(s):

Ntu Games ◽

The Core

Download Full-text

Weighted values and the core

International Journal of Game Theory ◽

10.1007/bf01240250 ◽

1992 ◽

Vol 21 (1) ◽

pp. 27-39 ◽

Cited By ~ 43

Author(s):

D. Monderer ◽

D. Samet ◽

L. S. Shapley

Keyword(s):

The Core ◽

Weighted Values

Download Full-text

STABILITY OF THE CORE IN A CLASS OF NTU GAMES: A CHARACTERIZATION

International Game Theory Review ◽

10.1142/s0219198902000628 ◽

2002 ◽

Vol 04 (02) ◽

pp. 165-172 ◽

Cited By ~ 1

Author(s):

ANINDYA BHATTACHARYA ◽

AMIT K. BISWAS

Keyword(s):

Cooperative Games ◽

Stable Set ◽

Regularity Conditions ◽

Transferable Utility ◽

Large Core ◽

Von Neumann ◽

Ntu Games ◽

The Core ◽

Important Solution ◽

Transferable Utility Games

The core and the stable set are possibly the two most crucially important solution concepts for cooperative games. The relation between the two has been investigated in the context of symmetric transferable utility games and this has been related to the notion of large core. In this paper the relation between the von-Neumann–Morgenstern stability of the core and the largeness of it is investigated in the case of non-transferable utility (NTU) games. The main findings are that under certain regularity conditions, if the core of an NTU game is large then it is a stable set and for symmetric NTU games the core is a stable set if and only if it is large.

Download Full-text