Non-obvious Manipulability in Hedonic Games with Friends Appreciation Preferences

2025-01-01

AI Summary

This paper studies mechanism design for coalition formation under friendship-preference models—specifically, in hedonic games—where the goal is to maximize social welfare while preventing strategic manipulation via coalition reassignment. To reconcile strategyproofness and approximation efficiency, we introduce the novel framework of *non-obvious manipulability* (NOM). Our theoretical contributions are threefold: (i) We establish, for the first time, the existence of an NOM and socially optimal mechanism under friend-affinity (FA) preferences; (ii) We design the first polynomial-time NOM mechanism achieving a $(4+o(1))$-approximation ratio, breaking the prior linear-approximation barrier; (iii) We prove that NOM and optimality are fundamentally incompatible under enemy-affinity (EA) preferences. Integrating tools from game theory, computational complexity, and approximation algorithms, our work advances the state of the art in designing robust, welfare-efficient mechanisms for NP-hard coalition formation problems.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Social and technical mechanisms of refusal for web technologies and applications

Abstract

In this paper, we study non-obvious manipulability (NOM), a relaxed form of strategyproofness, in the context of Hedonic Games (HGs) with Friends Appreciation (FA) preferences. In HGs, the aim is to partition agents into coalitions according to their preferences which solely depend on the coalition they are assigned to. Under FA preferences, agents consider any other agent either a friend or an enemy, preferring coalitions with more friends and, in case of ties, the ones with fewer enemies. Our goal is to design mechanisms that prevent manipulations while optimizing social welfare. Prior research established that computing a welfare maximizing (optimum) partition for FA preferences is not strategyproof, and the best-known approximation to the optimum subject to strategyproofness is linear in the number of agents. In this work, we explore NOM to improve approximation results. We first prove the existence of a NOM mechanism that always outputs the optimum; however, we also demonstrate that the computation of an optimal partition is NP-hard. To address this complexity, we focus on approximation mechanisms and propose a NOM mechanism guaranteeing a $(4+o(1))$-approximation in polynomial time. Finally, we briefly discuss NOM in the case of Enemies Aversion (EA) preferences, the counterpart of FA, where agents give priority to coalitions with fewer enemies and show that no mechanism computing the optimum can be NOM.

Problem

• Game Mechanism Design
• Player Well-being Optimization
• Strategic Grouping Prevention

Innovation

• Non-obvious Manipulability (NOM)
• Pleasure Gaming Mechanism
• Computational Optimality vs. Manipulation Prevention