  Multi-agent networked linear dynamic systems have attracted attention of
researchers in power systems, intelligent transportation, and industrial
automation. The agents might cooperatively optimize a global performance
objective, resulting in social optimization, or try to satisfy their own
selfish objectives using a noncooperative differential game. However, in these
solutions, large volumes of data must be sent from system states to possibly
distant control inputs, thus resulting in high cost of the underlying
communication network. To enable economically-viable communication, a
game-theoretic framework is proposed under the \textit{communication cost}, or
\textit{sparsity}, constraint, given by the number of communicating
state/control input pairs. As this constraint tightens, the system transitions
from dense to sparse communication, providing the trade-off between dynamic
system performance and information exchange. Moreover, using the proposed
sparsity-constrained distributed social optimization and noncooperative game
algorithms, we develop a method to allocate the costs of the communication
infrastructure fairly and according to the agents' diverse needs for feedback
and cooperation. Numerical results illustrate utilization of the proposed
algorithms to enable and ensure economic fairness of wide-area control among
power companies.
