The Limits of Fairness of the Variational Generalized Nash Equilibrium
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911235731095552 |
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| author | Hall, Sophie Dörfler, Florian Nax, Heinrich H. Bolognani, Saverio |
| author_facet | Hall, Sophie Dörfler, Florian Nax, Heinrich H. Bolognani, Saverio |
| contents | Generalized Nash equilibrium (GNE) problems are commonly used to model strategic interactions between self-interested agents who are coupled in cost and constraints. Specifically, the variational GNE, a refinement of the GNE, is often selected as the solution concept due to its non-discriminatory treatment of agents by charging a uniform ``shadow price" for shared resources. We study the fairness concept of v-GNEs from a comparability perspective and show that it makes an implicit assumption of unit comparability of agent's cost functions, one of the strongest comparability notions. Further, we introduce a new solution concept, f-GNE in which a fairness metric is chosen a priori which is compatible with the comparability at hand. We introduce an electric vehicle charging game to demonstrate the fragility of v-GNE fairness and compare it to the f-GNE under various fairness metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03540 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Limits of Fairness of the Variational Generalized Nash Equilibrium Hall, Sophie Dörfler, Florian Nax, Heinrich H. Bolognani, Saverio Systems and Control Generalized Nash equilibrium (GNE) problems are commonly used to model strategic interactions between self-interested agents who are coupled in cost and constraints. Specifically, the variational GNE, a refinement of the GNE, is often selected as the solution concept due to its non-discriminatory treatment of agents by charging a uniform ``shadow price" for shared resources. We study the fairness concept of v-GNEs from a comparability perspective and show that it makes an implicit assumption of unit comparability of agent's cost functions, one of the strongest comparability notions. Further, we introduce a new solution concept, f-GNE in which a fairness metric is chosen a priori which is compatible with the comparability at hand. We introduce an electric vehicle charging game to demonstrate the fragility of v-GNE fairness and compare it to the f-GNE under various fairness metrics. |
| title | The Limits of Fairness of the Variational Generalized Nash Equilibrium |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2504.03540 |