🤖 AI Summary
This paper investigates the existence, uniqueness, and stability of Nash equilibria in strategic games played by agents on multiplex and multilayer networks, with emphasis on how inter-layer coupling strength affects equilibrium robustness. We systematically formulate game-theoretic models for multiplex and multilayer networks, explicitly capturing cross-layer coordinated decision-making. Leveraging spectral graph theory and linear stability analysis, we derive spectral conditions for equilibrium uniqueness—expressed in terms of the largest and smallest eigenvalues of constituent layer adjacency matrices. We identify that equilibrium fragility in “networks-of-networks” arises from sensitivity to eigenvalue coupling. Furthermore, we quantify a dual topological regulation mechanism: network structure jointly governs both equilibrium existence and asymptotic stability. Our results provide an interpretable, intervention-aware framework for enhancing equilibrium robustness in complex interdependent systems—including multi-platform gaming ecosystems and cross-domain economic networks.
📝 Abstract
Network games provide a framework to study strategic decision making processes that are governed by structured interdependencies among agents. However, existing models do not account for environments in which agents simultaneously interact over multiple networks, or when agents operate over multiple action dimensions. In this paper, we propose new models of multiplex network games to capture the different modalities of interactions among strategic agents, and multilayer network games to capture their interactions over multiple action dimensions. We explore how the properties of the constituent networks of a multiplex/multilayer network can undermine or support the existence, uniqueness, and stability of the game's Nash equilibria. Notably, we highlight that both the largest and smallest eigenvalues of the constituent networks (reflecting their connectivity and two-sidedness, respectively) are instrumental in determining the uniqueness of the multiplex/multilayer network game's equilibrium. Together, our findings shed light on the reasons for the fragility of equilibria when agents interact over networks of networks, and point out potential interventions to alleviate them.