# Robustness against Agent Failure in Hedonic Games

## TL;DR

This paper investigates the robustness of stable outcomes in hedonic games against agent failures, proposing new criteria and demonstrating efficient decision procedures for certain classes of these games.

## Contribution

It introduces a novel robustness criterion for stability in hedonic games and provides efficient algorithms for symmetric friend-oriented and additively separable games.

## Key findings

- Efficiently deciding the existence of robust Nash stable outcomes under multiple deletions.
- Robust individual stability under single-agent deletion can be guaranteed in symmetric additively separable games.
- Symmetric additively separable games always admit an individually stable, robust outcome.

## Abstract

We study how stability can be maintained even after any set of at most k players leave their groups, in the context of hedonic games. While stability properties ensure an outcome to be robust against players' deviations, it has not been considered how an unexpected change caused by a sudden deletion of players affects stable outcomes. In this paper, we propose a novel criterion that reshapes stability form robustness aspect. We observe that some stability properties can be no longer preserved even when a single agent is removed. However, we obtain positive results by focusing on symmetric friend-oriented hedonic games. We prove that we can efficiently decide the existence of robust outcomes with respect to Nash stability under deletion of any number of players or contractual individual stability under deletion of a single player. We also show that symmetric additively separable games always admit an individual stable outcome that is robust with respect to individual rationality.