An interactive approach for solving Nash cooperative continuous static games (NCCSG)

Elshafei, Mervat M.

doi:10.12988/ijcms.2007.07116

Cited by 7 publications

(9 citation statements)

References 6 publications

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“…In addition, the cost functions and limitations are the only pieces of information available to each player. Elshafei [9] demonstrated an interactive method for solving Nash Cooperative Continuous Static Games, as well as the first-of-its-kind stability set that corresponds to the reached compromised solution. Khalifa and ZeinEldein [10] suggested an interactive technique for solving cooperative continuous static games with fuzzy parameter coefficients in the objective functions.…”

Section: Introductionmentioning

confidence: 99%

“…Farooqui and Niazi [15] published a comprehensive multidisciplinary assessment and classification of game theory models of complicated agent interactions. Based on compromise programming and the compromise weights method, an interactive method for solving Nash continuous cooperative static games was proposed by Sasikala and Kumaraghuru [16]. (NCCSTGs).…”

Section: Introductionmentioning

confidence: 99%

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On Stackelberg Leader with Min-Max Followers to Solve Fuzzy Continuous Static Games

Khalifa

Pamučar

Alburaikan

et al. 2022

Journal of Function Spaces

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This study attempts to introduce continuous static games with fuzzy parameters. Piecewise quadratic fuzzy numbers (PQFNs) are used to represent the fuzzy parameters. The close interval approximation of the PQFNs, which is one of the most accurate approximations, is applied. To overcome the problem, Stackelberg leaders with min-max follower’s solutions are examined. The given solution is accompanied by a parametric analysis. An algorithm for identifying the first-kind stability set is presented. Finally, to demonstrate and clarify the method’s steps, a numerical example is given

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Stackelberg Leader with Min-Max Followers to Solve Fuzzy Continuous Static Games

Khalifa

Pamučar

Alburaikan

et al. 2022

Journal of Function Spaces

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“…In addition, the information that is available to every player contains the cost functions and constraints. To solve Nash Cooperative Continuous Static Games, Elshafei [11] established an interactive approach and fixed on the first-kind corresponding's stability set to the obtained compromise solution. Several articles were developed for the game's theory by an enormous of research, and for more details about such studies, we refer to read the articles mentioned in [12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

On Stability of Continuous Cooperative Static Games with Possibilistic Parameters in the Objective Functions

Garg

Edalatpanah

El-Morsy

et al. 2022

Computational Intelligence and Neuroscience

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The objective of this paper is to present a novel idea about the continuous possibilistic cooperative static game (Poss-CCSTG). The proposed Poss-CCSTG is a continuous cooperative static game (CCSTG) in which parameter associated with the cost functions of the players involves the possibility measures. The considered Poss-CCSTG is converted into the crisp α-CCSTG problem by using the α-cuts and hence into the multiple objective nonlinear programming problem. To solve the formulated α-CCSTG problem, an interactive approach is presented in the study with the use of the reference direction method. Further, the Lexicographic weighted Tchebycheff model is derived to obtain the weights. Also, a parametric study corresponding to the α-possibly optimal solution is defined and determined. Finally, a decision-maker can compare their desired solution with the attainable reference point and the weak efficient solution. The presented model is illustrated with a numerical example and its advantages are stated.

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“…Mallozzi and Morgan [18] introduced ɛ-mixed approaches for CSG. El Shafei [19] proposed a new formulation of large scale CSG and explained how they can solve the mentioned problem by the concept of PMS and in [20] suggested an interactive compromise programming for a kind of Cooperative CSG (CCSG). Kenneth et al [21] designated some methods for solving all solutions of polynomial systems and then using these compute the equilibrium manifold of a kind of CSG, see also [22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

A New Methodology for Solving Piecewise Quadratic Fuzzy Cooperative Continuous Static Games

Xiao

Zhang

Lin

et al. 2022

Advances in Mathematical Physics

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This paper deals with n -players fuzzy cooperative continuous static games (FCCSGs). The cost function coefficients are characterized by piecewise quadratic fuzzy numbers. One of the best approximate intervals, namely, the inexact interval of the piecewise quadratic fuzzy number is used. Furthermore, we proposed a new methodology based on the weighted Tchebycheff method to solve CCSG with n -players. The advantages of the approach are the ability to enable the decision-maker to have satisfactory solution and applied for different real-world problems with various types of fuzzy numbers. There is also a stability set of the first kind without differentiability for the optimal compromise solution that was found. In the future, the proposed methodology could be used in different types of real-world problems and multiple decision-makers. This proposed work can also be extended to hypersoft set, fuzzy hypersoft sets, intuitionistic hypersoft sets, bipolar hypersoft sets, and pythagorean hypersoft sets. At the end, a numerical example is given to demonstrate the computational efficiency of the proposed method.

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An interactive approach for solving Nash cooperative continuous static games (NCCSG)

Cited by 7 publications

References 6 publications

On Stackelberg Leader with Min-Max Followers to Solve Fuzzy Continuous Static Games

On Stackelberg Leader with Min-Max Followers to Solve Fuzzy Continuous Static Games

On Stability of Continuous Cooperative Static Games with Possibilistic Parameters in the Objective Functions

A New Methodology for Solving Piecewise Quadratic Fuzzy Cooperative Continuous Static Games

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