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

Abstract: Generalized Nash equilibrum (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 it's 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.