scholarly journals The Shapley Values on Fuzzy Coalition Games with Concave Integral Form

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Jinhui Pang ◽  
Xiang Chen ◽  
Shujin Li
Keyword(s):  
Cooperative Game ◽  
Integral Form ◽  
Simple Calculation ◽  
Calculation Formula ◽  
Concave Integral ◽  
Shapley Values ◽  
Linear Aggregation ◽  
Fuzzy Game ◽  
Expected Values

A generalized form of a cooperative game with fuzzy coalition variables is proposed. The character function of the new game is described by the Concave integral, which allows players to assign their preferred expected values only to some coalitions. It is shown that the new game will degenerate into the Tsurumi fuzzy game when it is convex. The Shapley values of the proposed game have been investigated in detail and their simple calculation formula is given by a linear aggregation of the Shapley values on subdecompositions crisp coalitions.

scholarly journals Integral Representations of Cooperative Game with Fuzzy Coalitions

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jinhui Pang ◽  
Xiang Chen
Keyword(s):  
Characteristic Function ◽  
Explicit Formula ◽  
Cooperative Game ◽  
Integral Representations ◽  
New Class ◽  
Concave Integral ◽  
Fuzzy Game ◽  
Fuzzy Coalitions ◽  
Expected Values ◽  
Special Case

Classical extensions of fuzzy game models are based on various integrals, such as Butnariu game and Tsurumi game. A new class of symmetric extension of fuzzy game with fuzzy coalition variables is put forward with Concave integral, where players’ expected values are on a partial set of coalitions. Some representations and properties of some limited models are compared in this paper. The explicit formula of characteristic function determined by coalition variables is given. Moreover, a calculation approach of imputations is discussed in detail. The new game could be regarded as a general form of cooperative game. Furthermore, the fuzzy game introduced by Tsurumi is a special case of the proposed game when game is convex.

scholarly journals The Cores for Fuzzy Games Represented by the Concave Integral

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Jinhui Pang ◽  
Shujin Li
Keyword(s):  
Cooperative Games ◽  
Characteristic Functions ◽  
Game Model ◽  
Explicit Formulas ◽  
The Core ◽  
Concave Integral ◽  
Fuzzy Games ◽  
Fuzzy Game ◽  
Expected Values ◽  
Fuzzy Core

We propose a new fuzzy game model by the concave integral by assigning subjective expected values to random variables in the interval[0,1]. The explicit formulas of characteristic functions which are determined by coalition variables are discussed in detail. After illustrating some properties of the new game, its fuzzy core is defined; this is a generalization of crisp core. Moreover, we give a further discussion on the core for the new games. Some notions and results from classical games are extended to the model. The nonempty fuzzy core is given in terms of the fuzzy convexity. Our results develop some known fuzzy cooperative games.

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)

Axiomatization of Shapley Values of Fagle and Kern Type on Set Systems

2008 ◽  
Vol 12 (5) ◽  
pp. 409-415 ◽  
Author(s):  
Aoi Honda ◽  
◽  
Yoshiaki Okazaki
Keyword(s):  
Cooperative Game ◽  
Shapley Value ◽  
Potential Application ◽  
Set Systems ◽  
Shapley Values

We propose axiomatizing a generalized Shapley value of games for potential application to games on set systems satisfying the condition of normality. This encompasses both the original Shapley value and Faigle and Kern's Shapley value, which is generalized for a cooperative game defined on a subcoalition.

scholarly journals The core and superdifferential of a fuzzy TU-cooperative game

2020 ◽  
Vol 12 (2) ◽  
pp. 20-35
Author(s):  
Валерий Александрович Васильев ◽  
Valery Vasil'ev
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Subdifferential Calculus ◽  
The Core ◽  
Side Payments ◽  
Weak Homogeneity ◽  
Fuzzy Game

In the paper, we consider conditions providing coincidence of the cores and superdifferentials of fuzzy cooperative games with side payments. It turned out that one of the most simple sufficient conditions consists of weak homogeneity. Moreover, by applying so-called S*-representation of a fuzzy game introduced by the author, we show that for any vwith nonempty core C(v) there exists some game u such that C(v) coincides with the superdifferential of u. By applying subdifferential calculus we describe a structure of the core forboth classic fuzzy extensions of the ordinary cooperative game (e.g., Aubin and Owen extensions) and for some new continuations, like Harsanyi extensions and generalized Airport game.

Development of an Efficient Tool for Evaluating Dose at Through-Holes

2020 ◽  
Author(s):  
Tatsuya Watanabe ◽  
Hironobu Iwanami ◽  
Tomoharu Hashimoto ◽  
Ryuichi Tayama
Keyword(s):  
Nuclear Power ◽  
Power Plants ◽  
Gamma Ray ◽  
Integration Method ◽  
Computation Time ◽  
Simple Calculation ◽  
Detailed Calculation ◽  
Calculation Formula ◽  
Evaluation Point ◽  
Kernel Integration

Abstract In the design of nuclear power plants, it is demanded to quickly and calculate gamma ray scattering line (streaming) from the penetrating portion provided in the shielding such as electrical cables and ducts. However, when conducting gamma-ray streaming calculations from multiple penetrations, MCNP, a detailed calculation code, requires a long calculation time. This is due to the nature of MCNP, where many particles must reach the evaluation point when calculating in order for the results to be within an acceptable accuracy. To shorten the computation time, an analysis code utilizing a simple calculation method is necessary. Thus, we have developed a new method and a simple calculation tool (SVD-Dorc) for streaming computation. This method combines dose rate at an evaluation point with point kernel integration method and a simple streaming calculation formula for straight cylindrical ducts. Properties of SVD-Dorc are as follows: • Point kernel integration method • Simple streaming calculation formula for straight cylindrical ducts • Manual and automatic meshing of rectangular and cylindrical sources • Differentiation between direct line and non-direct sources • 3D drawing of input data • File output The validity of SVD-Dorc was confirmed by comparison with MCNP calculations and measured values from benchmark tests [2].

Public resources allocation using an uncertain cooperative game among vulnerable groups

Kybernetes ◽  
2019 ◽  
Vol 48 (8) ◽  
pp. 1606-1625 ◽  
Author(s):  
Pei Liang ◽  
Junhua Hu ◽  
Yongmei Liu ◽  
Xiaohong Chen
Keyword(s):  
Resource Allocation ◽  
Cooperative Game ◽  
Shapley Value ◽  
Choquet Integral ◽  
Convex Combination ◽  
Integral Form ◽  
Vulnerable Groups ◽  
Content Type ◽  
Public Resource ◽  
Public Resources

Purpose This paper aims to solve the problem of public resource allocation among vulnerable groups by proposing a new method called uncertain α-coordination value based on uncertain cooperative game. Design/methodology/approach First, explicit forms of uncertain Shapley value with Chouqet integral form and uncertain centre-of-gravity of imputation-set (CIS) value are defined separately on the basis of uncertainty theory and cooperative game. Then, a convex combination of the two values above called the uncertain α-coordination value is used as the best solution. This study proves that the proposed methods meet the basic properties of cooperative game. Findings The uncertain α-coordination value is used to solve a public medical resource allocation problem in fuzzy coalitions and uncertain payoffs. Compared with other methods, the α-coordination value can solve such problem effectively because it balances the worries of vulnerable group’s further development and group fairness. Originality/value In this paper, an extension of classical cooperative game called uncertain cooperative game is proposed, in which players choose any level of participation in a game and relate uncertainty with the value of the game. A new function called uncertain α-Coordination value is proposed to allocate public resources amongst vulnerable groups in an uncertain environment, a topic that has not been explored yet. The definitions of uncertain Shapley value with Choquet integral form and uncertain CIS value are proposed separately to establish uncertain α-Coordination value.

Cooperative game with fuzzy coalition and payoff value in the generalized integral form

2017 ◽  
Vol 33 (6) ◽  
pp. 3641-3651 ◽  
Author(s):  
Xiaohui Yu ◽  
Qiang Zhang ◽  
Zhen Zhou
Keyword(s):  
Cooperative Game ◽  
Integral Form

scholarly journals Using Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2021
Author(s):  
Hsien-Chung Wu
Keyword(s):  
Genetic Algorithms ◽  
Multiobjective Optimization ◽  
Cooperative Game ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Payoff Function ◽  
Pareto Optimal ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Shapley Values

This paper proposes a new methodology to solve multiobjective optimization problems by invoking genetic algorithms and the concept of the Shapley values of cooperative games. It is well known that the Pareto-optimal solutions of multiobjective optimization problems can be obtained by solving the corresponding weighting problems that are formulated by assigning some suitable weights to the objective functions. In this paper, we formulated a cooperative game from the original multiobjective optimization problem by regarding the objective functions as the corresponding players. The payoff function of this formulated cooperative game involves the symmetric concept, which means that the payoff function only depends on the number of players in a coalition and is independent of the role of players in this coalition. In this case, we can reasonably set up the weights as the corresponding Shapley values of this formulated cooperative game. Under these settings, we can obtain the so-called Shapley–Pareto-optimal solution. In order to choose the best Shapley–Pareto-optimal solution, we used genetic algorithms by setting a reasonable fitness function.

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