Stability in Online Coalition Formation

TL;DR

This paper explores online coalition formation, focusing on stability rather than social welfare, and provides a comprehensive analysis of algorithms' effectiveness in achieving stable structures in additively separable hedonic games.

Contribution

It introduces the first thorough study of online stability in coalition formation, highlighting the limitations of both deterministic and randomized algorithms.

Findings

Deterministic algorithms can achieve stability in certain cases.

Randomized algorithms face fundamental limitations in online stability.

The results establish clear boundaries between possible and impossible online stability outcomes.

Abstract

Coalition formation is concerned with the question of how to partition a set of agents into disjoint coalitions according to their preferences. Deviating from most of the previous work, we consider an online variant of the problem, where agents arrive in sequence. Whenever an agent arrives, they must be assigned to a coalition immediately and irrevocably. The scarce existing literature on online coalition formation has focused on maximizing social welfare, a demanding requirement, even in the offline setting. Instead, we seek to achieve \emph{stable} coalition structures online and treat the most common stability concepts based on deviations by single agents and groups of agents. We present a comprehensive picture in additively separable hedonic games, leading to dichotomies, where positive results are obtained by deterministic algorithms and negative results even hold for randomized algorithms.