scholarly journals Axiomatic results and dynamic processes for two weighted indexes under fuzzy transferable-utility behavior

2022 ◽  
Vol 12 (1) ◽  
pp. 1
Author(s):  
Yu-Hsien Liao
Keyword(s):  
Dynamic Processes ◽  
Excess Functions ◽  
Transferable Utility ◽  
Transferable Utility Games

<p style='text-indent:20px;'>By considering the supreme-utilities and the weights simultaneously under fuzzy behavior, we propose two indexes on fuzzy transferable-utility games. In order to present the rationality for these two indexes, we define extended reductions to offer several axiomatic results and dynamics processes. Based on different consideration, we also adopt excess functions to propose alternative formulations and related dynamic processes for these two indexes respectively.</p>

A weighted power distribution mechanism under fuzzy behavior systems

2021 ◽  
pp. 1-12
Author(s):  
Yu-Hsien Liao
Keyword(s):  
Power Distribution ◽  
Dynamic Processes ◽  
Alternative Formulation ◽  
Excess Functions ◽  
Transferable Utility ◽  
Payoff Vector ◽  
Weighted Index ◽  
Behavior Systems ◽  
Transferable Utility Games ◽  
Traditional Game

In real situations, players might represent administrative areas of different scales; players might have different activity abilities. Thus, we propose an extension of the Banzhaf-Owen index in the framework of fuzzy transferable-utility games by considering supreme-utilities and weights simultaneously, which we name the weighted fuzzy Banzhaf-Owen index. Here we adopt three existing notions from traditional game theory and reinterpret them in the framework of fuzzy transferable-utility games. The first one is that this weighted index could be represented as an alternative formulation in terms of excess functions. The second is that, based on an reduced game and related consistency, we offer an axiomatic result to present the rationality of this weighted index. Finally, we introduce two dynamic processes to illustrate that this weighted index could be reached by players who start from an arbitrary efficient payoff vector and make successive adjustments.

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 socially stable core in structured transferable utility games

2007 ◽  
Vol 59 (1) ◽  
pp. 85-104 ◽  
Author(s):  
P. Jean-Jacques Herings ◽  
Gerard van der Laan ◽  
Dolf Talman
Keyword(s):  
Transferable Utility ◽  
Stable Core ◽  
Transferable Utility Games

The Family of Least Square Values for Transferable Utility Games

1998 ◽  
Vol 24 (1-2) ◽  
pp. 109-130 ◽  
Author(s):  
Luis M. Ruiz ◽  
Federico Valenciano ◽  
Jose M. Zarzuelo
Keyword(s):  
Least Square ◽  
Transferable Utility ◽  
The Family ◽  
Transferable Utility Games ◽  
Least Square Values
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