Core, Shapley Value, and Weber Set

Game Theory ◽  
2008 ◽  
pp. 259-269
Keyword(s):  
Shapley Value ◽  
Weber Set

scholarly journals Convex Interval Games

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
S. Z. Alparslan Gök ◽  
R. Branzei ◽  
S. Tijs
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Allocation Scheme ◽  
Weber Set ◽  
The Shapley Value ◽  
Interval Games

Convex interval games are introduced and characterizations are given. Some economic situations leading to convex interval games are discussed. The Weber set and the Shapley value are defined for a suitable class of interval games and their relations with the interval core for convex interval games are established. The notion of population monotonic interval allocation scheme (pmias) in the interval setting is introduced and it is proved that each element of the Weber set of a convex interval game is extendable to such a pmias. A square operator is introduced which allows us to obtain interval solutions starting from the corresponding classical cooperative game theory solutions. It turns out that on the class of convex interval games the square Weber set coincides with the interval core.

A novel q-rung orthopair fuzzy TODIM approach for multi-criteria group decision making based on Shapley value and relative entropy

2021 ◽  
Vol 40 (1) ◽  
pp. 235-250
Author(s):  
Liuxin Chen ◽  
Nanfang Luo ◽  
Xiaoling Gou
Keyword(s):  
Decision Making ◽  
Relative Entropy ◽  
Group Decision Making ◽  
Shapley Value ◽  
Group Decision ◽  
Similarity Measures ◽  
Entropy Measure ◽  
Shapley Values ◽  
Interactive Relationship ◽  
The Difference

In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.

Profit distribution of liner alliance based on shapley value

2021 ◽  
pp. 1-5
Author(s):  
Bin Guo ◽  
Shengyue Hao ◽  
Guangmei Cao ◽  
Honghu Gao
Keyword(s):  
Decision Making ◽  
Customer Satisfaction ◽  
Shapley Value ◽  
Case Analysis ◽  
Distribution Method ◽  
New Model ◽  
Profit Distribution ◽  
Scientific Decision ◽  
Stable Development

Profit distribution plays an important role in the sustainable and stable development of liner alliances, this paper tries to solve the profit distribution issues in the liner alliance based on Shapley Value Method. Meanwhile, seeing that there is little consideration from the customer satisfaction, this paper establishes a new model by revising Shapley Value Method to distribute the profit of liner alliances from the perspectives of suppliers and customers and carry out verification through case analysis. The profit distribution method proposed in the paper is helpful to the reasonable profit distribution of liner alliance. It ensures the continuity and stability of liner alliance and provides a scientific decision-making basis for the profit distribution of liner alliance.

Allocating Positions Fairly: Auctions and Shapley Value

2021 ◽  
pp. 105315
Author(s):  
Matt Van Essen ◽  
John Wooders
Keyword(s):  
Shapley Value
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