  In this paper, the problem of network connectivity is studied for an
adversarial Internet of Battlefield Things (IoBT) system in which an attacker
aims at disrupting the connectivity of the network by choosing to compromise
one of the IoBT nodes at each time epoch. To counter such attacks, an IoBT
defender attempts to reestablish the IoBT connectivity by either deploying new
IoBT nodes or by changing the roles of existing nodes. This problem is
formulated as a dynamic multistage Stackelberg connectivity game that extends
classical connectivity games and that explicitly takes into account the
characteristics and requirements of the IoBT network. In particular, the
defender's payoff captures the IoBT latency as well as the sum of weights of
disconnected nodes at each stage of the game. Due to the dependence of the
attacker's and defender's actions at each stage of the game on the network
state, the feedback Stackelberg solution (FSE) is used to solve the IoBT
connectivity game. Then, sufficient conditions under which the IoBT system will
remain connected, when the FSE solution is used, are determined analytically.
Numerical results show that the expected number of disconnected sensors, when
the FSE solution is used, decreases up to 62% compared to a baseline scenario
in which a Stackelberg game with no feedback is used, and up to 57% compared to
a baseline equal probability policy.
