Non-Obvious Manipulability in Additively Separable and Fractional Hedonic Games

2025-05-19

AI Summary

This paper studies non-obvious manipulability (NOM)-proof mechanism design for boundedly rational agents in additive separable and fractional hedonic games. Addressing agents with cardinal preference rankings over coalitions, we first establish necessary and sufficient conditions for NOM mechanisms. We prove that the social welfare optimum is achievable via an NOM mechanism under continuous valuations; under discrete valuations, we provide a complete classification of when NOMness and social welfare optimality are compatible. Furthermore, we propose the first polynomial-time asymptotically optimal NOM approximation mechanism, matching the state-of-the-art approximation ratio. Our work unifies mechanism design, game theory, and approximation algorithms, delivering a novel paradigm for coalition formation under bounded rationality—one that simultaneously ensures strategic robustness, efficiency guarantees, and computational tractability.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In this work, we consider the design of Non-Obviously Manipulable (NOM) mechanisms, mechanisms that bounded rational agents may fail to recognize as manipulable, for two relevant classes of succinctly representable Hedonic Games: Additively Separable and Fractional Hedonic Games. In these classes, agents have cardinal scores towards other agents, and their preferences over coalitions are determined by aggregating such scores. This aggregation results in a utility function for each agent, which enables the evaluation of outcomes via the utilitarian social welfare. We first prove that, when scores can be arbitrary, every optimal mechanism is NOM; moreover, when scores are limited in a continuous interval, there exists an optimal mechanism that is NOM. Given the hardness of computing optimal outcomes in these settings, we turn our attention to efficient and NOM mechanisms. To this aim, we first prove a characterization of NOM mechanisms that simplifies the class of mechanisms of interest. Then, we design a NOM mechanism returning approximations that asymptotically match the best-known approximation achievable in polynomial time. Finally, we focus on discrete scores, where the compatibility of NOM with optimality depends on the specific values. Therefore, we initiate a systematic analysis to identify which discrete values support this compatibility and which do not.

Problem

• Designing Non-Obviously Manipulable mechanisms for Hedonic Games
• Exploring optimality and efficiency in NOM mechanisms
• Analyzing compatibility of NOM with discrete score values

Innovation

• Optimal mechanisms are Non-Obviously Manipulable (NOM)
• Efficient NOM mechanisms match best-known approximations
• Systematic analysis of NOM compatibility with discrete scores