On class of non-transferable utility cooperative differential games with continuous updating

Wang, Zeyang; Petrosian, Ovanes

doi:10.3934/jdg.2020020

Cited by 8 publications

(3 citation statements)

References 18 publications

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“…Kada et al [17], proposed a mathematical model that describes the dynamic of a population that reacts in the spread of the E-game infection and study the stability of endemic equilibrium point of gaming disorder. Zeyang Wang et al [18], considers and describes the class of cooperative differential games with non-transferable utilities and the process of construction of the optimal Pareto strategy with continuous updating. Many studies and research in the social sciences have focused on this subject [19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of the gaming disorder model with media coverage: optimal control approach

Kada¹,

Kouidere²,

Balatif³

et al. 2023

Math. Model. Comput.

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In this article, we propose a PEARM mathematical model to depict the dynamic of a population that reacts in the spread of the gaming disorder with media coverage. The basic reproduction number and existence of free equilibrium point and endimec equilibrium point are obtained with same fundamental properties of the model including existence and positivity as well as boundedness of equilibria are investigated. By using Routh–Hurwitz criteria, the local stability of free equilibrium point and endimec equilibrium point are obtained. Also, we propose an optimal strategy to implement the optimal campaigns through directing children and adolescents to educational and entertaining alternative means, and creating centers to restore the rehabilitation of addicts to electronic games. The existence of the optimal control are obtained by Pontryagain's maximum principle. Finally, some numerical simulations are also performed to illustrate the theoretical analysis of our results, using Matlab software. Our results show that media coverage is an effective measure to quit electronic gaming disorder.

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Section: Introductionmentioning

confidence: 99%

Mathematical modeling of the gaming disorder model with media coverage: optimal control approach

Kada¹,

Kouidere²,

Balatif³

et al. 2023

Math. Model. Comput.

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“…Khalifa and Kumar [23] studied the cooperative continuous static games in a crisp environment, defined them, and found the firstkind stability set corresponding to the solution without differentiability. Several researchers [24][25][26][27][28][29] have recently enriched the theory of cooperative games by considering the degree of uncertainties in the analysis.…”

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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“…For example, Brida and Cayssials [8] generalize the classical model of determination of production prices for two commodities by introducing dynamics generated by the possibility that the port rate can be computed using prices of different stages. Wang and Petrosian [9] consider and describe the class of cooperative differential games with nontransferable utility and the process of construction of the optimal Pareto strategy with continuous updating. Guo and Li [10] establish a new online game addiction model with low-and high-risk exposure and use the optimal control theory to study the optimal solution problem with three kinds of control measures (isolation, education, and treatment).…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Approach of Discrete Mathematical Modeling of the Spread of Gaming Disorder in Morocco and Cost-Effectiveness Analysis

Kada

Khajji

Balatif

et al. 2021

Discrete Dynamics in Nature and Society

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We highlight and study in this paper the phenomenon of the spread of addiction to electronic games, where the addict goes through stages before reaching the degree of addiction. In order to model this phenomenon, we have divided people into four groups, which are potential gamers, engaged gamers, addicted gamers, and gamers who have recovered from addiction. We propose a discrete mathematical model with control strategies using three controls that represent, respectively, u k , which represents awareness of the dangers of electronic games through written and visual media; v k , which represents the effort to direct children and adolescents to educational and entertaining alternative means; and w k , which represents creating rehabilitation centers for addicts to quit electronic game addiction. To characterize optimal controls, we use Pontryagin’s maximum principle and the system of optimality solved by an iterative method. Finally, numerical simulations are presented with and without controls. Using a cost-effectiveness analysis, we will show that the control that represents the creation of rehabilitation centers for gaming addicts is the most cost-effective strategy to control the spread of gaming addiction.

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On class of non-transferable utility cooperative differential games with continuous updating

Cited by 8 publications

References 18 publications

Mathematical modeling of the gaming disorder model with media coverage: optimal control approach

Mathematical modeling of the gaming disorder model with media coverage: optimal control approach

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

Optimal Control Approach of Discrete Mathematical Modeling of the Spread of Gaming Disorder in Morocco and Cost-Effectiveness Analysis

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