Existence of an Aumann–Maschler fuzzy bargaining set and fuzzy kernels in TU fuzzy games

2018 ◽  
Vol 349 ◽  
pp. 53-63 ◽  
Author(s):  
Jiuqiang Liu ◽  
Xiaodong Liu ◽  
Yan Huang ◽  
Wenbo Yang
Keyword(s):  
Bargaining Set ◽  
Fuzzy Games

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.

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.

scholarly journals The bargaining set for almost-convex games

2012 ◽  
Vol 225 (1) ◽  
pp. 83-89
Author(s):  
Jesús Getán ◽  
Josep M. Izquierdo ◽  
Jesús Montes ◽  
Carles Rafels
Keyword(s):  
Convex Games ◽  
Bargaining Set ◽  
Almost Convex
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