A Strategic Implementation of the Shapley Value for the Nested Cost-Sharing Problem

2016 ◽  
Vol 19 (1) ◽  
pp. 219-233 ◽  
Author(s):  
YOUNGSUB CHUN ◽  
CHENG-CHENG HU ◽  
CHUN-HSIEN YEH
Keyword(s):  
Shapley Value ◽  
Cost Sharing ◽  
The Shapley Value ◽  
Strategic Implementation

scholarly journals Cost Sharing Models in Game Theory = Költségelosztási modellek a játékelméletben

2021 ◽  
Author(s):  
◽  
Anna Ráhel Radványi
Keyword(s):  
Water Management ◽  
Game Theory ◽  
Cooperative Game ◽  
Shortest Path ◽  
Shapley Value ◽  
Cost Sharing ◽  
Average Cost ◽  
Fair Allocation ◽  
Sharing Rule ◽  
The Shapley Value

In our thesis we examined economic situations modeled with rooted trees and directed, acyclic graphs. In the presented problems the collaboration of economic agents (players) incurred costs or created a profit, and we have sought answers to the question of \fairly" distributing this common cost or profit. We have formulated properties and axioms describing our expecta- tions of a \fair" allocation. We have utilized cooperative game theoretical methods for modeling. After the introduction, in Chapter 2 we analyzed a real-life problem and its possible solutions. These solution proposals, namely the average cost- sharing rule, the serial cost sharing rule, and the restricted average cost- sharing rule have been introduced by Aadland and Kolpin (2004). We have also presented two further water management problems that arose during the planning of the economic development of Tennessee Valley, and discussed solution proposals for them as well (Straffinn and Heaney, 1981). We analyzed if these allocations satisfied the properties we associated with the notion of \fairness". In Chapter 3 we introduced the fundamental notions and concepts of cooperative game theory. We defined the core (Shapley, 1955; Gillies, 1959) and the Shapley value (Shapley, 1953), that play an important role in finding a \fair" allocation. In Chapter 4 we presented the class of fixed-tree game and relevant ap- plications from the domain of water management. In Chapter 5 we discussed the classes of airport and irrigation games, and the characterizations of these classes. We extended the results of Dubey (1982) and Moulin and Shenker (1992) on axiomatization of the Shapley value on the class of airport games to the class of irrigation games. We have \translated" the axioms used in cost allocation literature to the axioms corresponding to TU games, thereby providing two new versions of the results of Shapley (1953) and Young (1985). In Chapter 6 we introduced the upstream responsibility games and char- acterized the game class. We have shown that Shapley's and Young's char- acterizations are valid on this class as well. In Chapter 7 we discussed shortest path games and have shown that this game class is equal to the class of monotone games. We have shown that further axiomatizations of the Shapley value, namely Shapley (1953)'s, Young (1985)'s, Chun (1989)'s, and van den Brink (2001)'s characterizations are valid on the class of shortest path games.

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)

Sign in / Sign up

Export Citation Format

Share Document