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.

翻译：网络博弈提供了研究受智能体间结构化相互依赖关系支配的策略性决策过程的框架。然而，现有模型未考虑智能体同时在多个网络上交互的环境，或智能体在多个行动维度上运作的情形。本文提出多重网络博弈的新模型，以刻画策略性智能体间不同模态的交互，以及多层网络博弈模型，以刻画其在多个行动维度上的交互。我们探究多重/多层网络的组成网络特性如何削弱或支撑博弈纳什均衡的存在性、唯一性与稳定性。值得注意的是，我们强调组成网络的最大与最小特征值（分别反映其连通性与双边性）在决定多重/多层网络博弈均衡唯一性中起关键作用。综上，本研究成果揭示了当智能体在“网络之网络”交互时均衡脆弱性的原因，并指出了缓解此类问题的潜在干预措施。