← 研踪 PaperTrailarXiv:2611.09060 · v1
Fair Selection of Generalized Nash Equilibria: A Comparability Perspective
首次提交 2026-11-06 14:36
版本更新 2026-11-06 14:36
雷达观测 2026-11-09 11:19
摘要
Generalized Nash equilibrium (GNE) problems model self-interested agents coupled through their costs and shared constraints, and arise throughout control applications that allocate a scarce common resource. Such problems typically admit a continuum of equilibria, so any implementation must \emph{select} one. This selection is not neutral: it decides how the cost of the shared constraint is distributed among the agents, a decision often expected to be fair. The variational GNE (v-GNE), which charges all agents a uniform shadow price, is the conventional choice and is frequently advocated as fair. Through the lens of \emph{comparability} from social choice theory, we show that the GNE set itself requires no inter-agent comparability of costs, whereas the v-GNE implicitly assumes cardinal unit comparability, one of the stronger notions. We then introduce the fair GNE (f-GNE), which selects an equilibrium by explicitly optimizing a fairness metric matched to the comparability at hand, and give constructive routes to compute it for single-constraint and linear-quadratic games. An electric-vehicle charging game serves as a running example throughout this self-contained tutorial.
作者备注：Book chapter, 25 pages, 4 figures. To appear in Socio-Inspired and Socially Aware Control for Complex Systems, Springer
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v1 · 2026-11-06 14:36 · 最新观测版本
Fair Selection of Generalized Nash Equilibria: A Comparability Perspective
Generalized Nash equilibrium (GNE) problems model self-interested agents coupled through their costs and shared constraints, and arise throughout control applications that allocate a scarce common resource. Such problems typically admit a continuum of equilibria, so any implementation must \emph{select} one. This selection is not neutral: it decides how the cost of the shared constraint is distributed among the agents, a decision often expected to be fair. The variational GNE (v-GNE), which charges all agents a uniform shadow price, is the conventional choice and is frequently advocated as fair. Through the lens of \emph{comparability} from social choice theory, we show that the GNE set itself requires no inter-agent comparability of costs, whereas the v-GNE implicitly assumes cardinal unit comparability, one of the stronger notions. We then introduce the fair GNE (f-GNE), which selects an equilibrium by explicitly optimizing a fairness metric matched to the comparability at hand, and give constructive routes to compute it for single-constraint and linear-quadratic games. An electric-vehicle charging game serves as a running example throughout this self-contained tutorial.
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