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.

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.

Reactive and Semi-Reactive Bargaining Sets for Games with Restricted Cooperation

2020 ◽  
Vol 22 (03) ◽  
pp. 2050001
Author(s):  
Natalia Naumova
Keyword(s):  
Sufficient Conditions ◽  
Existence Results ◽  
Simple Games ◽  
Bargaining Set ◽  
Tu Games ◽  
Restricted Cooperation ◽  
Generalized Kernel ◽  
Existence Conditions ◽  
Necessary And Sufficient ◽  
Bargaining Sets

Generalizations of reactive and semi-reactive bargaining sets of TU games are defined for the case when objections and counter-objections are permitted not between singletons but between elements of a family of coalitions [Formula: see text] and can use coalitions from [Formula: see text]. Necessary and sufficient conditions on [Formula: see text], [Formula: see text] that ensure existence results for generalizations of the reactive bargaining set and of the semi-reactive barganing set at each TU game [Formula: see text] with nonnegative values are obtained. The existence conditions for the generalized reactive bargaining set do not coincide with existence conditions for the generalized kernel and coincide with conditions for the generalized semi-reactive bargaining set only if [Formula: see text] and [Formula: see text]. The conditions for the generalized semi-reactive bargaining set coincide with conditions for the generalized classical bargaining set that were described in the previous papers of the author. For monotonic [Formula: see text], the condition on [Formula: see text] for existence of the generalized semi-reactive bargaining sets on the class of games with nonnegative values is also necessary and sufficient on the class of simple games, but similar result for the generalized classical bargaining sets is proved only for [Formula: see text].

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.

On the core, nucleolus and bargaining sets of cooperative games with fuzzy payoffs

2019 ◽  
Vol 36 (6) ◽  
pp. 6129-6142 ◽  
Author(s):  
Xia Zhang ◽  
Hao Sun ◽  
Genjiu Xu ◽  
Dongshuang Hou
Keyword(s):  
Cooperative Games ◽  
The Core ◽  
Bargaining Sets

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.

The core and the bargaining set in glove-market games

2003 ◽  
Vol 32 (2) ◽  
pp. 189-204 ◽  
Author(s):  
Yevgenia Apartsin ◽  
Ron Holzman
Keyword(s):  
Bargaining Set ◽  
Market Games ◽  
The Core

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.

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
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