scholarly journals The Fair Proportion is a Shapley Value on phylogenetic networks too

2018 ◽  
Author(s):  
Tomás M. Coronado ◽  
Gabriel Riera ◽  
Francesc Rosselló
Keyword(s):  
Phylogenetic Tree ◽  
Shapley Value ◽  
Phylogenetic Diversity ◽  
Phylogenetic Networks ◽  
Fair Proportion ◽  
Simple Measure ◽  
The Shapley Value

AbstractThe Fair Proportion of a species in a phylogenetic tree is a very simple measure that has been used to assess its value relative to the overall phylogenetic diversity represented by the tree. It has recently been proved by Fuchs and Jin to be equal to the Shapley Value of the coallitional game that sends each subset of species to its rooted Phylogenetic Diversity in the tree. We prove in this paper that this result extends to the natural translations of the Fair Proportion and the rooted Phylogenetic Diversity to rooted phylogenetic networks. We also generalize to rooted phylogenetic networks the expression for the Shapley Value of the unrooted Phylogenetic Diversity game on a phylogenetic tree established by Haake, Kashiwada and Su.

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.

scholarly journals A new basis and the Shapley value

2016 ◽  
Vol 80 ◽  
pp. 21-24 ◽  
Author(s):  
Koji Yokote ◽  
Yukihiko Funaki ◽  
Yoshio Kamijo
Keyword(s):  
Shapley Value ◽  
The Shapley Value

COPING WITH UNCERTAINTY IN n-PERSON GAMES

2000 ◽  
Vol 08 (05) ◽  
pp. 503-523 ◽  
Author(s):  
SILVIU GUIASU
Keyword(s):  
Characteristic Function ◽  
Security Council ◽  
Shapley Value ◽  
Statistical Equilibrium ◽  
Individual Rationality ◽  
Von Neumann ◽  
Minimum Deviation ◽  
The Shapley Value ◽  
Un Security Council ◽  
Person Game

A solution of n-person games is proposed, based on the minimum deviation from statistical equilibrium subject to the constraints imposed by the group rationality and individual rationality. The new solution is compared with the Shapley value and von Neumann-Morgenstern's core of the game in the context of the 15-person game of passing and defeating resolutions in the UN Security Council involving five permanent members and ten nonpermanent members. A coalition classification, based on the minimum ramification cost induced by the characteristic function of the game, is also presented.

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