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arXiv · 2504.03540

The Limits of "Fairness'' of the Variational Generalized Nash Equilibrium

Sophie Hall·Florian Dörfler·Heinrich H. Nax·Saverio Bolognani
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Abstract

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.

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Sophie Hall, Florian Dörfler, Heinrich H. Nax, Saverio Bolognani. 2025-04-04. The Limits of "Fairness'' of the Variational Generalized Nash Equilibrium. https://arxiv.org/abs/2504.03540

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