Stable Invitations

TL;DR

This paper studies the problem of selecting the largest stable group of agents for an event, considering agents' preferences and strategic behavior, and analyzes the computational complexity and mechanism design aspects.

Contribution

It introduces the problem of maximum stable invitations, analyzing its computational complexity and strategic considerations in preference reporting.

Findings

Determines the complexity of finding maximum stable invitations.

Analyzes the impact of strategic misreporting on invitation stability.

Provides insights into mechanism design for stable invitations.

Abstract

We consider the situation in which an organizer is trying to convene an event, and needs to choose a subset of agents to be invited. Agents have preferences over how many attendees should be at the event and possibly also who the attendees should be. This induces a stability requirement: All invited agents should prefer attending to not attending, and all the other agents should not regret being not invited. The organizer's objective is to find the invitation of maximum size subject to the stability requirement. We investigate the computational complexity of finding the maximum stable invitation when all agents are truthful, as well as the mechanism design problem when agents may strategically misreport their preferences.