Computing the Shapley Value of Threshold Cardinality Matching Games

2017 ◽  
pp. 174-185
Author(s):  
Lei Zhao ◽  
Xin Chen ◽  
Qizhi Fang
Keyword(s):  
Shapley Value ◽  
The Shapley Value ◽  
Matching Games

scholarly journals The Tractability of the Shapley Value over Bounded Treewidth Matching Games

2017 ◽  
Author(s):  
Gianluigi Greco ◽  
Francesco Lupia ◽  
Francesco Scarcello
Keyword(s):  
Polynomial Time ◽  
Shapley Value ◽  
Open Problem ◽  
Positive Answer ◽  
Coalitional Games ◽  
Solution Concepts ◽  
Bounded Treewidth ◽  
The Shapley Value ◽  
Matching Games

Matching games form a class of coalitional games that attracted much attention in the literature. Indeed, several results are known about the complexity of computing over them {solution concepts}. In particular, it is known that computing the Shapley value is intractable in general, formally #P-hard, and feasible in polynomial time over games defined on trees. In fact, it was an open problem whether or not this tractability result holds over classes of graphs properly including acyclic ones. The main contribution of the paper is to provide a positive answer to this question, by showing that the Shapley value is tractable for matching games defined over graphs having bounded treewidth. The proposed technique has been implemented and tested on classes of graphs having different sizes and treewidth at most three.

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.

Shapley Ranking of Wines

2012 ◽  
Vol 7 (2) ◽  
pp. 169-180 ◽  
Author(s):  
Victor Ginsburgh ◽  
Israël Zang
Keyword(s):  
Game Theory ◽  
Unique Solution ◽  
Cooperative Game ◽  
Shapley Value ◽  
Rank Order ◽  
Jel Classification ◽  
Ranking Method ◽  
The Shapley Value ◽  
Shapley Values

AbstractWe suggest a new game-theory-based ranking method for wines, in which the Shapley Value of each wine is computed, and wines are ranked according to their Shapley Values. Judges should find it simpler to use, since they are not required to rank order or grade all the wines, but merely to choose the group of those that they find meritorious. Our ranking method is based on the set of reasonable axioms that determine the Shapley Value as the unique solution of an underlying cooperative game. Unlike in the general case, where computing the Shapley Value could be complex, here the Shapley Value and hence the final ranking, are straightforward to compute. (JEL Classification: C71, D71, D78)

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