Title of article :
Stability of fixed points of set-valued mappings and strategic stability of Nash equilibria
Author/Authors :
Xiang ، Shuwen - Guizhou University , Xia ، Shunyou - Guizhou University , He ، Jihao - Guizhou University , Yang ، Yanlong - Guizhou University , Liu ، Chenwei - Guizhou University
Pages :
13
From page :
3599
To page :
3611
Abstract :
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 y, which is even used to study any noncooperative game.
Keywords :
Stability , Nash equilibria , fixed point , strong , perturbation , stable set
Journal title :
Journal of Nonlinear Science and Applications
Serial Year :
2017
Journal title :
Journal of Nonlinear Science and Applications
Record number :
2476676
Link To Document :
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