The Shapley value for the network game with pairwise interactions

2015 ◽  
Author(s):  
Maria Bulgakova ◽  
Leon Petrosyan
Keyword(s):  
Shapley Value ◽  
Pairwise Interactions ◽  
The Shapley Value ◽  
Network Game

scholarly journals Non-Zero Sum Network Games with Pairwise Interactions

2021 ◽  
Vol 14 ◽  
pp. 38-48
Author(s):  
Mariia A. Bulgakova ◽  
Keyword(s):  
Shapley Value ◽  
Network Formation ◽  
Network Games ◽  
Zero Sum Games ◽  
Pairwise Interactions ◽  
Formation Stage ◽  
The Shapley Value ◽  
Cooperative Solutions ◽  
Zero Sum ◽  
Network Form

In the paper non-zero sum games on networks with pairwise interactions are investigated. The first stage is network formation stage, where players chose their preferable set of neighbours. In all following stages simultaneous non-zero sum game appears between connected players in network. As cooperative solutions the Shapley value and τ -value are considered. Due to a construction of characteristic function both formulas are simpli ed. It is proved, that the coeffcient λ in τ -value is independent from network form and number of players or neighbours and is equal to 1/2 . Also it is proved that in this type of games on complete network the Shapley value and τ -value are coincide.

Trade with Technology Spillover: A Dynamic Network Game Analysis

2020 ◽  
pp. 2050011
Author(s):  
David W. K. Yeung ◽  
Leon A. Petrosyan ◽  
Yingxuan Zhang
Keyword(s):  
Shapley Value ◽  
General Class ◽  
Dynamic Network ◽  
Technology Spillover ◽  
Network Games ◽  
Game Analysis ◽  
The Shapley Value ◽  
Positive Externalities ◽  
Network Game ◽  
Representative Model

This paper presents a general class of dynamic network games to analyze trade with technology spillover. Due to the fact that the benefits of technology spillover are not fully accrued to the technology developer, the positive externalities are under-exploited. The cooperative solution yields an optimal outcome. To reflect the contributions of individual agents to the network, the Shapley value is used as a solution optimality principle in sharing the cooperative gains. A time-consistent payoff imputation procedure is derived to maintain the Shapley value at each stage of the cooperation. A representative model based on the general class of network games with explicit functional form is given. This is the first time that trade with technology spillover is studied in the framework of dynamic network games, further studies along this line are expected.

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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