  Network connectivity plays an important role in the information exchange
between different agents in the multi-level networks. In this paper, we
establish a game-theoretic framework to capture the uncoordinated nature of the
decision-making at different layers of the multi-level networks. Specifically,
we design a decentralized algorithm that aims to maximize the algebraic
connectivity of the global network iteratively. In addition, we show that the
designed algorithm converges to a Nash equilibrium asymptotically and yields an
equilibrium network. To study the network resiliency, we introduce three
adversarial attack models and characterize their worst-case impacts on the
network performance. Case studies based on a two-layer mobile robotic network
are used to corroborate the effectiveness and resiliency of the proposed
algorithm and show the interdependency between different layers of the network
during the recovery processes.
