Stability in Random Hedonic Games

TL;DR

This paper analyzes stability in random hedonic games, showing high probability of stable partitions under certain conditions and explaining the rarity of Nash-stable partitions in large random settings.

Contribution

It introduces a new random model for hedonic games and provides algorithms and probabilistic analysis for stability concepts, addressing computational and existence challenges.

Findings

Efficient algorithm for stable partitions with high probability

High likelihood of stability in large random games under certain concepts

Nash-stable partitions are rare in large random hedonic games

Abstract

Partitioning a large group of employees into teams can prove difficult because unsatisfied employees may want to transfer to other teams. In this case, the team (coalition) formation is unstable and incentivizes deviation from the proposed structure. Such a coalition formation scenario can be modeled in the framework of hedonic games and a significant amount of research has been devoted to the study of stability in such games. Unfortunately, stable coalition structures are not guaranteed to exist in general and their practicality is further hindered by computational hardness barriers. We offer a new perspective on this matter by studying a random model of hedonic games. For three prominent stability concepts based on single-agent deviations, we provide a high probability analysis of stability in the large agent limit. Our first main result is an efficient algorithm that outputs an individually and contractually Nash-stable partition with high probability. Our second main result is that the probability that a random game admits a Nash-stable partition tends to zero. Our approach resolves the two major downsides associated with individual stability and contractual Nash stability and reveals agents acting single-handedly are usually to blame for instabilities.