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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2504.03208 |
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| _version_ | 1866912540368306176 |
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| author | Matsuo, Shota Kume, Keita Yamada, Isao |
| author_facet | Matsuo, Shota Kume, Keita Yamada, Isao |
| contents | The equilibrium selection problem in the variational Generalized Nash Equilibrium Problem (v-GNEP) has been reported as an optimization problem defined over the solution set of v-GNEP, called in this paper the lower-level v-GNEP. However, to make such a selection fair for every player, we have to rely on an unrealistic assumption, that is, the availability of a trusted center that does not induce any bias among players. In this paper, to ensure fairness for every player even in the process of equilibrium selection, we propose a new equilibrium selection problem, named the upper-level v-GNEP. The proposed upper-level v-GNEP is formulated as a v-GNEP defined over the solution set of the lower-level v-GNEP. We also present an iterative algorithm, of guaranteed convergence to a solution of the upper-level v-GNEP, as an application of the hybrid steepest descent method to a fixed point set characterization of the solution of the lower-level v-GNEP. Numerical experiments illustrate the proposed equilibrium selection and algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03208 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hierarchical Variational Inequality Problem for Noncooperative Game-Theoretic Selection of Generalized Nash Equilibrium Matsuo, Shota Kume, Keita Yamada, Isao Optimization and Control 47H09, 47J26, 49J40, 91A10, and 91A11 The equilibrium selection problem in the variational Generalized Nash Equilibrium Problem (v-GNEP) has been reported as an optimization problem defined over the solution set of v-GNEP, called in this paper the lower-level v-GNEP. However, to make such a selection fair for every player, we have to rely on an unrealistic assumption, that is, the availability of a trusted center that does not induce any bias among players. In this paper, to ensure fairness for every player even in the process of equilibrium selection, we propose a new equilibrium selection problem, named the upper-level v-GNEP. The proposed upper-level v-GNEP is formulated as a v-GNEP defined over the solution set of the lower-level v-GNEP. We also present an iterative algorithm, of guaranteed convergence to a solution of the upper-level v-GNEP, as an application of the hybrid steepest descent method to a fixed point set characterization of the solution of the lower-level v-GNEP. Numerical experiments illustrate the proposed equilibrium selection and algorithm. |
| title | Hierarchical Variational Inequality Problem for Noncooperative Game-Theoretic Selection of Generalized Nash Equilibrium |
| topic | Optimization and Control 47H09, 47J26, 49J40, 91A10, and 91A11 |
| url | https://arxiv.org/abs/2504.03208 |