Revisiting the Fairness of Pure Nash Equilibria of Round-Robin

Georgios Amanatidis; Haris Aziz; Georgios Birmpas; Federico Fusco; Stefano Leonardi; Rebecca Reiffenhäuser

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arXiv · 2610.23686

Revisiting the Fairness of Pure Nash Equilibria of Round-Robin

Georgios Amanatidis·Haris Aziz·Georgios Birmpas·Federico Fusco·Stefano Leonardi·Rebecca Reiffenhäuser

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Abstract

We prove that for additive valuations, not every pure Nash equilibrium of the Round-Robin mechanism induces an allocation that is envy-free up to one good (EF1) with respect to the agents' true valuations. This corrects an earlier claim of Amanatidis et al. (WINE 2021; Math. Oper. Res. 2024). On the positive side, every pure Nash equilibrium of every fixed recursively balanced picking sequence mechanism induces an allocation that is $1/2$-EF1 and proportional up to one good (PROP1). We prove the approximate EF1 guarantee through a potential function comparing two executions, and the proportionality guarantee via a deviation that preserves the agent's most valuable goods. We also give a family of Round Robin equilibria showing that it is not possible to have a strictly better guarantee than $2/3$-EF1 for all equilibria.

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Georgios Amanatidis, Haris Aziz, Georgios Birmpas, Federico Fusco, Stefano Leonardi, Rebecca Reiffenhäuser. 2026-10-16. Revisiting the Fairness of Pure Nash Equilibria of Round-Robin. https://arxiv.org/abs/2610.23686

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