United We Fall: On the Nash Equilibria of Multiplex and Multilayer Network Games
CoRR(2024)
摘要
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.
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