Stable and Envy-free Partitions in Hedonic Games
Stable and Envy-free Partitions in Hedonic Games
Nathanaƫl Barrot, Makoto Yokoo
Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence
Main track. Pages 67-73.
https://doi.org/10.24963/ijcai.2019/10
In this paper, we study coalition formation in hedonic games through the fairness criterion of envy-freeness.
Since the grand coalition is always envy-free, we focus on the conjunction of envy-freeness with stability notions.
We first show that, in symmetric and additively separable hedonic games, an individually stable and justified envy-free partition may not exist and deciding its existence is NP-complete.
Then, we prove that the top responsiveness property guarantees the existence of a Pareto optimal, individually stable, and envy-free partition, but it is not sufficient for the conjunction of core stability and envy-freeness.
Finally, under bottom responsiveness, we show that deciding the existence of an individually stable and envy-free partition is NP-complete, but a Pareto optimal and justified envy-free partition always exists.
Keywords:
Agent-based and Multi-agent Systems: Cooperative Games
Agent-based and Multi-agent Systems: Algorithmic Game Theory