scholarly journals Null or Zero Players: The Difference between the Shapley Value and the Egalitarian Solution

2004 ◽  
Author(s):  
René van den Brink
Keyword(s):  
Shapley Value ◽  
The Shapley Value ◽  
The Difference ◽  
Egalitarian Solution

scholarly journals Attaining Fairness in Communication for Omniscience

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 109
Author(s):  
Ni Ding ◽  
Parastoo Sadeghi ◽  
David Smith ◽  
Thierry Rakotoarivelo
Keyword(s):  
Polynomial Time ◽  
Shapley Value ◽  
Data Exchange ◽  
Source Coding ◽  
Extreme Points ◽  
Mean Value ◽  
The Core ◽  
Coding Schemes ◽  
The Shapley Value ◽  
Egalitarian Solution

This paper studies how to attain fairness in communication for omniscience that models the multi-terminal compress sensing problem and the coded cooperative data exchange problem where a set of users exchange their observations of a discrete multiple random source to attain omniscience—the state that all users recover the entire source. The optimal rate region containing all source coding rate vectors that achieve omniscience with the minimum sum rate is shown to coincide with the core (the solution set) of a coalitional game. Two game-theoretic fairness solutions are studied: the Shapley value and the egalitarian solution. It is shown that the Shapley value assigns each user the source coding rate measured by their remaining information of the multiple source given the common randomness that is shared by all users, while the egalitarian solution simply distributes the rates as evenly as possible in the core. To avoid the exponentially growing complexity of obtaining the Shapley value, a polynomial-time approximation method is proposed which utilizes the fact that the Shapley value is the mean value over all extreme points in the core. In addition, a steepest descent algorithm is proposed that converges in polynomial time on the fractional egalitarian solution in the core, which can be implemented by network coding schemes. Finally, it is shown that the game can be decomposed into subgames so that both the Shapley value and the egalitarian solution can be obtained within each subgame in a distributed manner with reduced complexity.

A NOTE ON THE COMPUTATION OF THE SHAPLEY VALUE FOR VON NEUMANN–MORGENSTERN MARKET GAMES

2010 ◽  
Vol 12 (03) ◽  
pp. 287-291 ◽  
Author(s):  
VITO FRAGNELLI ◽  
ANA MECA
Keyword(s):  
Shapley Value ◽  
Simple Expression ◽  
Market Game ◽  
Market Games ◽  
Von Neumann ◽  
Allocation Procedure ◽  
The Shapley Value ◽  
The Difference

We consider a von Neumann–Morgenstern market game and present a simple expression for the Shapley value via decomposition as the difference of an airport game and an extended airport game. The resulting formula has a useful interpretation for designing an allocation procedure among the agents.

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.

Query Games in Databases

2021 ◽  
Vol 50 (1) ◽  
pp. 78-85
Author(s):  
Ester Livshits ◽  
Leopoldo Bertossi ◽  
Benny Kimelfeld ◽  
Moshe Sebag
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
The Shapley Value ◽  
Computational Aspects ◽  
Aggregate Query ◽  
Boolean Query

Database tuples can be seen as players in the game of jointly realizing the answer to a query. Some tuples may contribute more than others to the outcome, which can be a binary value in the case of a Boolean query, a number for a numerical aggregate query, and so on. To quantify the contributions of tuples, we use the Shapley value that was introduced in cooperative game theory and has found applications in a plethora of domains. Specifically, the Shapley value of an individual tuple quantifies its contribution to the query. We investigate the applicability of the Shapley value in this setting, as well as the computational aspects of its calculation in terms of complexity, algorithms, and approximation.

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