Friend- and Enemy-oriented Hedonic Games With Strangers Full Version

TL;DR

This paper introduces two new classes of hedonic games involving friends, enemies, and strangers, analyzing their stability properties and computational complexity of related decision problems.

Contribution

It formalizes FOHGS and EOHGS models, characterizes the computational hardness of stability verification, and proves existence results for certain stable partitions.

Findings

Necessarily internally stable partitions always exist.

Hardness results for verifying stability notions.

Conditions for necessary contractual individual stability.

Abstract

We introduce friend- and enemy-oriented hedonic games with strangers (FOHGS and EOHGS respectively), two classes of hedonic games wherein agents are classified as friends, enemies, or strangers under the assumption that strangers will become either friends or enemies ex post facto. For several notions of stability in FOHGS and EOHGS, we characterize the hardness of verification for possible and necessary stability. We characterize the hardness of deciding whether possibly and necessarily X stable partitions exist for a given stability notion X. We prove that necessarily internally stable partitions always exist and provide sufficient conditions for necessary contractual individual stability.