Existence and stability of weakly Pareto-Nash equilibrium for generalized multiobjective multi-leader–follower games

Jia, Wensheng; Xiang, Shuwen; He, Jingsong; Yong-sheng, Yang

doi:10.1007/s10898-014-0178-y

Cited by 29 publications

(11 citation statements)

References 20 publications

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“…Yu and Xiang [26] proposed an essential set for Nash equilibria and proved the existence of essential component in the second direction by considering perturbations of payoff functions of players. There is a lot of researches about using the essential component to discuss the stability of Nash equilibria (see, [1,2,8,17,18,24,25,27]). However, there are two drawbacks in the second way.…”

Section: Introductionmentioning

confidence: 99%

Stability of fixed points of set-valued mappings and strategic stability of Nash equilibria

Xiang¹,

Xia²,

Yang³

et al. 2017

J. Nonlinear Sci. Appl.

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In this paper, we mainly focus on the stability of Nash equilibria to any perturbation of strategy sets. A larger perturbation, strong δ-perturbation, will be proposed for set-valued mapping. The class of perturbed games considered in the definition of strong δ-perturbation is richer than those considered in many other definitions of stability of Nash equilibria. The strong δ-perturbation of the best reply correspondence will be used to define an appropriate stable set for Nash equilibria, called SBR-stable set. As an SBR-stable set is stable to any strong δ-perturbation and, various perturbations of strategy sets are not beyond the range of strong δ-perturbation, it has the stability that various stable sets possess, such as fully stable set, stable set, quasistable set, and essential set. An SBR-stable set is stable to any perturbation of strategy sets, so it will provide convenience for study in strategic stability, which is even used to study any noncooperative game.

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Section: Introductionmentioning

confidence: 99%

Stability of fixed points of set-valued mappings and strategic stability of Nash equilibria

Xiang¹,

Xia²,

Yang³

et al. 2017

J. Nonlinear Sci. Appl.

Self Cite

View full text Add to dashboard Cite

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“…When F i , Γ is real-valued functions and S " R `, condition (i) holds naturally. Hence, if V " R, S " R `and Θ i " X i , the above result reduces to Corollary 3.8 in [18].…”

Section: Proof Define a Function φPyqmentioning

confidence: 81%

“…Yang and Yu [17] obtained an essential component of the set of its weakly Pareto-Nash equilibrium points by a Ky Fan inequality of vector-valued functions. Jia et al [18] obtained existence and stability of weakly Pareto-Nash equilibrium for generalized multiobjective multi-leader-follower games. Hung et al [19] considered the generic stability of vector quasi-equilibrium problems on Hadamard manifolds.…”

Section: Introductionmentioning

confidence: 99%

Existence and Generic Stability of Strong Noncooperative Equilibria of Vector-Valued Games

Chang

Chen

2021

Mathematics

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In this paper, we obtain an existence theorem of general strong noncooperative equilibrium point of vector-valued games, in which every player maximizes all goals. We also obtain an existence theorem of strong equilibrium point of vector-valued games with single-leader–multi-follower framework by using the upper semicontinuous of parametric strong noncooperative equilibrium point set of the followers. Moreover, we obtain some results on the generic stability of general strong noncooperative equilibrium point vector-valued games.

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“…Theorem 1 [30]: For a multilateral Stackelberg game, if X, Y i (i = 1, 2, • • • , n) are non-empty tight convex subsets in two locally convex Hausdorff linear topological spaces respectively, the equilibrium solution exists when each player satisfies the following conditions:…”

Section: Existence Of Nash Equilibriummentioning

confidence: 99%

Subsidy and Pricing Model of Electric Vehicle Sharing Based on Two-Stage Stackelberg Game – A Case Study in China

Chen

2019

Applied Sciences

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Electric vehicle sharing provides an effective way to improve the traffic situation and relieve environmental pressure. The government subsidy policy and the car-sharing operator’s pricing strategy are the key factors that affect the large-scale application of electric vehicle sharing. To address this issue, a subsidy and pricing model for electric vehicle sharing based on the two-stage Stackelberg game is proposed in this paper according to the current situation in China. First, an electric vehicle sharing operation mode under government participation is constructed. Then, a two-stage Stackelberg game model involving the government, the car-sharing operator and the consumers is proposed to determine the subsidy rates and pricing strategies. The improved particle swarm optimization algorithm is used to obtain the Nash equilibrium of the model. Also, the influence of private car cost and shared travel comfort on subsidy rates and pricing strategies is analyzed. Finally, the simulation of electric vehicle sharing in a town of China is carried out to investigate the performance of the proposed subsidy and price model. The simulation results show that the model rationally formulates subsidy policies and pricing strategies of the electric vehicle sharing to balance the interests of the three participants, mobilizing users’ enthusiasm while guaranteeing the benefits of the government and operator, making the overall benefit optimal.

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Existence and stability of weakly Pareto-Nash equilibrium for generalized multiobjective multi-leader–follower games

Cited by 29 publications

References 20 publications

Stability of fixed points of set-valued mappings and strategic stability of Nash equilibria

Stability of fixed points of set-valued mappings and strategic stability of Nash equilibria

Existence and Generic Stability of Strong Noncooperative Equilibria of Vector-Valued Games

Subsidy and Pricing Model of Electric Vehicle Sharing Based on Two-Stage Stackelberg Game – A Case Study in China

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